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Analysis\Normed\Operator\BoundedLinearMaps.lean
/- Copyright (c) 2018 Patrick Massot. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Patrick Massot, Johannes Hölzl -/ import Mathlib.Analysis.NormedSpace.Multilinear.Basic import Mathlib.Analysis.Normed.Ring.Units import Mathlib.Analysis.NormedSpace.OperatorNorm.Compl...
Analysis\Normed\Operator\Compact.lean
/- Copyright (c) 2022 Anatole Dedecker. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Anatole Dedecker -/ import Mathlib.Analysis.LocallyConvex.Bounded import Mathlib.Topology.Algebra.Module.StrongTopology /-! # Compact operators In this file we define compact linea...
Analysis\Normed\Operator\ContinuousLinearMap.lean
/- Copyright (c) 2019 Jan-David Salchow. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jan-David Salchow, Sébastien Gouëzel, Jean Lo -/ import Mathlib.Topology.Algebra.Module.Basic import Mathlib.Analysis.Normed.MulAction /-! # Constructions of continuous linear maps...
Analysis\Normed\Operator\LinearIsometry.lean
/- Copyright (c) 2021 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov, Frédéric Dupuis, Heather Macbeth -/ import Mathlib.Algebra.Star.Basic import Mathlib.Analysis.Normed.Group.Constructions import Mathlib.Analysis.Normed.Group.Submodul...
Analysis\Normed\Operator\WeakOperatorTopology.lean
/- Copyright (c) 2024 Frédéric Dupuis. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Frédéric Dupuis -/ import Mathlib.Analysis.LocallyConvex.WithSeminorms import Mathlib.Analysis.Normed.Module.Dual /-! # The weak operator topology This file defines a type copy of ...
Analysis\Normed\Order\Basic.lean
/- Copyright (c) 2020 Anatole Dedecker. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Anatole Dedecker, Yaël Dillies -/ import Mathlib.Algebra.Order.Group.TypeTags import Mathlib.Analysis.Normed.Field.Basic /-! # Ordered normed spaces In this file, we define classes...
Analysis\Normed\Order\Lattice.lean
/- Copyright (c) 2021 Christopher Hoskin. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Christopher Hoskin -/ import Mathlib.Analysis.Normed.Group.Constructions import Mathlib.Analysis.Normed.Group.Rat import Mathlib.Analysis.Normed.Group.Uniform import Mathlib.Topolo...
Analysis\Normed\Order\UpperLower.lean
/- Copyright (c) 2022 Yaël Dillies. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yaël Dillies -/ import Mathlib.Algebra.Order.Field.Pi import Mathlib.Algebra.Order.UpperLower import Mathlib.Analysis.Normed.Group.Pointwise import Mathlib.Analysis.Normed.Order.Basic im...
Analysis\Normed\Ring\Seminorm.lean
/- Copyright (c) 2022 María Inés de Frutos-Fernández. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: María Inés de Frutos-Fernández, Yaël Dillies -/ import Mathlib.Analysis.Normed.Field.Basic import Mathlib.Analysis.SpecialFunctions.Pow.Real /-! # Seminorms and norms ...
Analysis\Normed\Ring\SeminormFromBounded.lean
/- Copyright (c) 2024 María Inés de Frutos-Fernández. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: María Inés de Frutos-Fernández -/ import Mathlib.Analysis.Normed.Ring.Seminorm import Mathlib.Analysis.SpecialFunctions.Pow.Complex /-! # seminormFromBounded In this f...
Analysis\Normed\Ring\SeminormFromConst.lean
/- Copyright (c) 2024 María Inés de Frutos-Fernández. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: María Inés de Frutos-Fernández -/ import Mathlib.Analysis.Normed.Ring.Seminorm /-! # SeminormFromConst In this file, we prove [BGR, Proposition 1.3.2/2][bosch-guntze...
Analysis\Normed\Ring\Units.lean
/- Copyright (c) 2020 Heather Macbeth. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Heather Macbeth -/ import Mathlib.Topology.Algebra.Ring.Ideal import Mathlib.Analysis.SpecificLimits.Normed /-! # The group of units of a complete normed ring This file contains the...
Analysis\NormedSpace\AddTorsor.lean
/- Copyright (c) 2020 Joseph Myers. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joseph Myers, Yury Kudryashov -/ import Mathlib.Algebra.CharP.Invertible import Mathlib.Analysis.Normed.Module.Basic import Mathlib.Analysis.Normed.Group.AddTorsor import Mathlib.LinearA...
Analysis\NormedSpace\AddTorsorBases.lean
/- Copyright (c) 2021 Oliver Nash. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Oliver Nash -/ import Mathlib.Analysis.Normed.Module.FiniteDimension import Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional /-! # Bases in normed affine spaces. This file contains r...
Analysis\NormedSpace\AffineIsometry.lean
/- Copyright (c) 2021 Heather Macbeth. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Heather Macbeth -/ import Mathlib.Algebra.CharP.Invertible import Mathlib.Analysis.Normed.Operator.LinearIsometry import Mathlib.Analysis.Normed.Group.AddTorsor import Mathlib.Analysi...
Analysis\NormedSpace\BallAction.lean
/- Copyright (c) 2022 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov, Heather Macbeth -/ import Mathlib.Analysis.Normed.Field.UnitBall import Mathlib.Analysis.Normed.Module.Basic /-! # Multiplicative actions of/on balls and spheres Le...
Analysis\NormedSpace\ConformalLinearMap.lean
/- Copyright (c) 2021 Yourong Zang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yourong Zang -/ import Mathlib.Analysis.Normed.Module.Basic import Mathlib.Analysis.Normed.Operator.LinearIsometry /-! # Conformal Linear Maps A continuous linear map between `R`-norme...
Analysis\NormedSpace\Connected.lean
/- Copyright (c) 2023 Sébastien Gouëzel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sébastien Gouëzel -/ import Mathlib.Analysis.Convex.Topology import Mathlib.LinearAlgebra.Dimension.DivisionRing import Mathlib.Topology.Algebra.Module.Cardinality /-! # Connectedn...
Analysis\NormedSpace\ContinuousAffineMap.lean
/- Copyright (c) 2021 Oliver Nash. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Oliver Nash -/ import Mathlib.Analysis.NormedSpace.AffineIsometry import Mathlib.Topology.Algebra.ContinuousAffineMap import Mathlib.Analysis.NormedSpace.OperatorNorm.NormedSpace /-! # C...
Analysis\NormedSpace\DualNumber.lean
/- Copyright (c) 2023 Eric Wieser. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Eric Wieser -/ import Mathlib.Algebra.DualNumber import Mathlib.Analysis.Normed.Algebra.TrivSqZeroExt /-! # Results on `DualNumber R` related to the norm These are just restatements of ...
Analysis\NormedSpace\ENorm.lean
/- Copyright (c) 2020 Yury G. Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury G. Kudryashov -/ import Mathlib.Analysis.Normed.Module.Basic /-! # Extended norm In this file we define a structure `ENorm 𝕜 V` representing an extended norm (i.e., a norm ...
Analysis\NormedSpace\Extend.lean
/- Copyright (c) 2020 Ruben Van de Velde. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Ruben Van de Velde -/ import Mathlib.Algebra.Algebra.RestrictScalars import Mathlib.Analysis.NormedSpace.OperatorNorm.Basic import Mathlib.Analysis.RCLike.Basic /-! # Extending a ...
Analysis\NormedSpace\Extr.lean
/- Copyright (c) 2022 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov -/ import Mathlib.Analysis.Normed.Module.Ray import Mathlib.Topology.Order.LocalExtr /-! # (Local) maximums in a normed space In this file we prove the following lem...
Analysis\NormedSpace\FunctionSeries.lean
/- Copyright (c) 2022 Sébastien Gouëzel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sébastien Gouëzel -/ import Mathlib.Analysis.Normed.Group.InfiniteSum import Mathlib.Topology.Instances.ENNReal /-! # Continuity of series of functions We show that series of func...
Analysis\NormedSpace\HomeomorphBall.lean
/- Copyright (c) 2021 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov, Oliver Nash -/ import Mathlib.Topology.PartialHomeomorph import Mathlib.Analysis.Normed.Group.AddTorsor import Mathlib.Analysis.NormedSpace.Pointwise import Mathlib.D...
Analysis\NormedSpace\IndicatorFunction.lean
/- Copyright (c) 2020 Zhouhang Zhou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Zhouhang Zhou, Yury Kudryashov -/ import Mathlib.Algebra.Order.Group.Indicator import Mathlib.Analysis.Normed.Group.Basic /-! # Indicator function and norm This file contains a few si...
Analysis\NormedSpace\Int.lean
/- Copyright (c) 2021 Johan Commelin. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johan Commelin -/ import Mathlib.Analysis.Normed.Field.Basic /-! # The integers as normed ring This file contains basic facts about the integers as normed ring. Recall that `‖n‖` de...
Analysis\NormedSpace\MazurUlam.lean
/- Copyright (c) 2020 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov -/ import Mathlib.Topology.Instances.RealVectorSpace import Mathlib.Analysis.NormedSpace.AffineIsometry /-! # Mazur-Ulam Theorem Mazur-Ulam theorem states that an is...
Analysis\NormedSpace\MStructure.lean
/- Copyright (c) 2022 Christopher Hoskin. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Christopher Hoskin -/ import Mathlib.Algebra.Ring.Idempotents import Mathlib.Analysis.Normed.Group.Basic import Mathlib.Order.Basic import Mathlib.Tactic.NoncommRing /-! # M-struc...
Analysis\NormedSpace\Pointwise.lean
/- Copyright (c) 2021 Sébastien Gouëzel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sébastien Gouëzel, Yaël Dillies -/ import Mathlib.Analysis.Normed.Group.Pointwise import Mathlib.Analysis.NormedSpace.Real /-! # Properties of pointwise scalar multiplication of se...
Analysis\NormedSpace\RCLike.lean
/- Copyright (c) 2021 Kalle Kytölä. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kalle Kytölä -/ import Mathlib.Analysis.RCLike.Basic import Mathlib.Analysis.NormedSpace.OperatorNorm.Basic import Mathlib.Analysis.NormedSpace.Pointwise /-! # Normed spaces over R or C...
Analysis\NormedSpace\Real.lean
/- Copyright (c) 2020 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov, Patrick Massot, Eric Wieser, Yaël Dillies -/ import Mathlib.Analysis.Normed.Module.Basic import Mathlib.Topology.Algebra.Module.Basic /-! # Basic facts about real (s...
Analysis\NormedSpace\RieszLemma.lean
/- Copyright (c) 2019 Jean Lo. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jean Lo, Yury Kudryashov -/ import Mathlib.Analysis.NormedSpace.Real import Mathlib.Analysis.Seminorm import Mathlib.Topology.MetricSpace.HausdorffDistance /-! # Applications of the Hausdorf...
Analysis\NormedSpace\SphereNormEquiv.lean
/- Copyright (c) 2023 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov -/ import Mathlib.Analysis.Normed.Module.Basic /-! # Homeomorphism between a normed space and sphere times `(0, +∞)` In this file we define a homeomorphism between n...
Analysis\NormedSpace\HahnBanach\Extension.lean
/- Copyright (c) 2020 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov, Heather Macbeth -/ import Mathlib.Analysis.Convex.Cone.Extension import Mathlib.Analysis.NormedSpace.RCLike import Mathlib.Analysis.NormedSpace.Extend import Mathlib....
Analysis\NormedSpace\HahnBanach\SeparatingDual.lean
/- Copyright (c) 2023 Sébastien Gouëzel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sébastien Gouëzel -/ import Mathlib.Analysis.NormedSpace.HahnBanach.Extension import Mathlib.Analysis.NormedSpace.HahnBanach.Separation import Mathlib.LinearAlgebra.Dual import Math...
Analysis\NormedSpace\HahnBanach\Separation.lean
/- Copyright (c) 2022 Bhavik Mehta. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Bhavik Mehta, Yaël Dillies -/ import Mathlib.Analysis.Convex.Cone.Extension import Mathlib.Analysis.Convex.Gauge import Mathlib.Topology.Algebra.Module.FiniteDimension import Mathlib.Top...
Analysis\NormedSpace\Multilinear\Basic.lean
/- Copyright (c) 2020 Sébastien Gouëzel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sébastien Gouëzel, Sophie Morel, Yury Kudryashov -/ import Mathlib.Analysis.NormedSpace.OperatorNorm.NormedSpace import Mathlib.Logic.Embedding.Basic import Mathlib.Data.Fintype.Car...
Analysis\NormedSpace\Multilinear\Curry.lean
/- Copyright (c) 2020 Sébastien Gouëzel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sébastien Gouëzel -/ import Mathlib.Analysis.NormedSpace.Multilinear.Basic /-! # Currying and uncurrying continuous multilinear maps We associate to a continuous multilinear map i...
Analysis\NormedSpace\OperatorNorm\Asymptotics.lean
/- Copyright (c) 2019 Jan-David Salchow. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jan-David Salchow, Sébastien Gouëzel, Jean Lo -/ import Mathlib.Analysis.NormedSpace.OperatorNorm.Basic import Mathlib.Analysis.Asymptotics.Asymptotics /-! # Asymptotic statements a...
Analysis\NormedSpace\OperatorNorm\Basic.lean
/- Copyright (c) 2019 Jan-David Salchow. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jan-David Salchow, Sébastien Gouëzel, Jean Lo -/ import Mathlib.Algebra.Algebra.Tower import Mathlib.Analysis.LocallyConvex.WithSeminorms import Mathlib.Topology.Algebra.Module.Stro...
Analysis\NormedSpace\OperatorNorm\Bilinear.lean
/- Copyright (c) 2019 Jan-David Salchow. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jan-David Salchow, Sébastien Gouëzel, Jean Lo -/ import Mathlib.Analysis.NormedSpace.OperatorNorm.Basic import Mathlib.Analysis.Normed.Operator.LinearIsometry import Mathlib.Analysi...
Analysis\NormedSpace\OperatorNorm\Completeness.lean
/- Copyright (c) 2019 Jan-David Salchow. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jan-David Salchow, Sébastien Gouëzel, Jean Lo -/ import Mathlib.Analysis.NormedSpace.OperatorNorm.Bilinear import Mathlib.Analysis.NormedSpace.OperatorNorm.NNNorm /-! # Operators o...
Analysis\NormedSpace\OperatorNorm\Mul.lean
/- Copyright (c) 2019 Jan-David Salchow. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jan-David Salchow, Sébastien Gouëzel, Jean Lo -/ import Mathlib.Analysis.NormedSpace.OperatorNorm.NormedSpace /-! # Results about operator norms in normed algebras This file (spl...
Analysis\NormedSpace\OperatorNorm\NNNorm.lean
/- Copyright (c) 2019 Jan-David Salchow. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jan-David Salchow, Sébastien Gouëzel, Jean Lo -/ import Mathlib.Analysis.NormedSpace.OperatorNorm.Basic /-! # Operator norm as an `NNNorm` Operator norm as an `NNNorm`, i.e. takin...
Analysis\NormedSpace\OperatorNorm\NormedSpace.lean
/- Copyright (c) 2019 Jan-David Salchow. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jan-David Salchow, Sébastien Gouëzel, Jean Lo -/ import Mathlib.Analysis.NormedSpace.OperatorNorm.Bilinear import Mathlib.Analysis.NormedSpace.OperatorNorm.NNNorm import Mathlib.Ana...
Analysis\NormedSpace\OperatorNorm\Prod.lean
/- Copyright (c) 2019 Jan-David Salchow. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jan-David Salchow, Sébastien Gouëzel, Jean Lo -/ import Mathlib.Analysis.NormedSpace.OperatorNorm.Bilinear /-! # Operator norm: Cartesian products Interaction of operator norm wit...
Analysis\NormedSpace\PiTensorProduct\InjectiveSeminorm.lean
/- Copyright (c) 2024 Sophie Morel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sophie Morel -/ import Mathlib.Analysis.NormedSpace.PiTensorProduct.ProjectiveSeminorm import Mathlib.LinearAlgebra.Isomorphisms /-! # Injective seminorm on the tensor of a finite famil...
Analysis\NormedSpace\PiTensorProduct\ProjectiveSeminorm.lean
/- Copyright (c) 2024 Sophie Morel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sophie Morel -/ import Mathlib.Analysis.NormedSpace.Multilinear.Basic import Mathlib.LinearAlgebra.PiTensorProduct /-! # Projective seminorm on the tensor of a finite family of normed s...
Analysis\ODE\Gronwall.lean
/- Copyright (c) 2020 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov -/ import Mathlib.Analysis.SpecialFunctions.ExpDeriv /-! # Grönwall's inequality The main technical result of this file is the Grönwall-like inequality `norm_le_gron...
Analysis\ODE\PicardLindelof.lean
/- Copyright (c) 2021 Yury G. Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury G. Kudryashov, Winston Yin -/ import Mathlib.Analysis.SpecialFunctions.Integrals import Mathlib.Topology.MetricSpace.Contracting /-! # Picard-Lindelöf (Cauchy-Lipschitz) Theo...
Analysis\RCLike\Basic.lean
/- Copyright (c) 2020 Frédéric Dupuis. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Frédéric Dupuis -/ import Mathlib.Algebra.Star.Order import Mathlib.Analysis.CStarAlgebra.Basic import Mathlib.Analysis.Normed.Operator.ContinuousLinearMap import Mathlib.Analysis.Nor...
Analysis\RCLike\Lemmas.lean
/- Copyright (c) 2020 Frédéric Dupuis. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Frédéric Dupuis -/ import Mathlib.Analysis.Normed.Module.FiniteDimension import Mathlib.Analysis.RCLike.Basic /-! # Further lemmas about `RCLike` -/ variable {K E : Type*} [RCLike ...
Analysis\SpecialFunctions\Arsinh.lean
/- Copyright (c) 2020 James Arthur. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: James Arthur, Chris Hughes, Shing Tak Lam -/ import Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv import Mathlib.Analysis.SpecialFunctions.Log.Basic /-! # Inverse of the sinh fu...
Analysis\SpecialFunctions\Bernstein.lean
/- Copyright (c) 2021 Scott Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Scott Morrison -/ import Mathlib.Analysis.SpecificLimits.Basic import Mathlib.RingTheory.Polynomial.Bernstein import Mathlib.Topology.ContinuousFunction.Polynomial import Mathlib.Topol...
Analysis\SpecialFunctions\CompareExp.lean
/- Copyright (c) 2022 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov -/ import Mathlib.Analysis.SpecialFunctions.Pow.Asymptotics import Mathlib.Analysis.Asymptotics.AsymptoticEquivalent import Mathlib.Analysis.Asymptotics.SpecificAsympt...
Analysis\SpecialFunctions\Exp.lean
/- Copyright (c) 2018 Chris Hughes. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Chris Hughes, Abhimanyu Pallavi Sudhir, Jean Lo, Calle Sönne -/ import Mathlib.Analysis.Complex.Asymptotics import Mathlib.Analysis.SpecificLimits.Normed /-! # Complex and real exponent...
Analysis\SpecialFunctions\ExpDeriv.lean
/- Copyright (c) 2018 Chris Hughes. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Chris Hughes, Abhimanyu Pallavi Sudhir, Jean Lo, Calle Sönne -/ import Mathlib.Analysis.Complex.RealDeriv import Mathlib.Analysis.Calculus.ContDiff.RCLike import Mathlib.Analysis.Calculu...
Analysis\SpecialFunctions\Exponential.lean
/- Copyright (c) 2021 Anatole Dedecker. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Anatole Dedecker, Eric Wieser -/ import Mathlib.Analysis.Normed.Algebra.Exponential import Mathlib.Analysis.Calculus.FDeriv.Analytic import Mathlib.Topology.MetricSpace.CauSeqFilter ...
Analysis\SpecialFunctions\ImproperIntegrals.lean
/- Copyright (c) 2023 David Loeffler. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: David Loeffler -/ import Mathlib.Analysis.SpecialFunctions.JapaneseBracket import Mathlib.Analysis.SpecialFunctions.Integrals import Mathlib.MeasureTheory.Group.Integral import Mathlib...
Analysis\SpecialFunctions\Integrals.lean
/- Copyright (c) 2021 Benjamin Davidson. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Benjamin Davidson -/ import Mathlib.MeasureTheory.Integral.FundThmCalculus import Mathlib.Analysis.SpecialFunctions.Trigonometric.ArctanDeriv import Mathlib.Analysis.SpecialFunction...
Analysis\SpecialFunctions\JapaneseBracket.lean
/- Copyright (c) 2022 Moritz Doll. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Moritz Doll -/ import Mathlib.Analysis.SpecialFunctions.Integrals import Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar import Mathlib.MeasureTheory.Integral.Layercake /-! # Japanese Brac...
Analysis\SpecialFunctions\NonIntegrable.lean
/- Copyright (c) 2021 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov -/ import Mathlib.Analysis.SpecialFunctions.Log.Deriv import Mathlib.MeasureTheory.Integral.FundThmCalculus /-! # Non integrable functions In this file we prove that...
Analysis\SpecialFunctions\PolarCoord.lean
/- Copyright (c) 2022 Sébastien Gouëzel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sébastien Gouëzel -/ import Mathlib.MeasureTheory.Function.Jacobian import Mathlib.MeasureTheory.Measure.Lebesgue.Complex import Mathlib.Analysis.SpecialFunctions.Trigonometric.Deri...
Analysis\SpecialFunctions\PolynomialExp.lean
/- Copyright (c) 2023 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov -/ import Mathlib.Algebra.Polynomial.Eval import Mathlib.Analysis.SpecialFunctions.Exp /-! # Limits of `P(x) / e ^ x` for a polynomial `P` In this file we prove that...
Analysis\SpecialFunctions\Polynomials.lean
/- Copyright (c) 2020 Anatole Dedecker. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Anatole Dedecker, Devon Tuma -/ import Mathlib.Algebra.Polynomial.Roots import Mathlib.Analysis.Asymptotics.AsymptoticEquivalent import Mathlib.Analysis.Asymptotics.SpecificAsymptoti...
Analysis\SpecialFunctions\SmoothTransition.lean
/- Copyright (c) 2020 Sébastien Gouëzel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sébastien Gouëzel, Yury Kudryashov -/ import Mathlib.Analysis.Calculus.Deriv.Inv import Mathlib.Analysis.Calculus.Deriv.Polynomial import Mathlib.Analysis.SpecialFunctions.ExpDeriv ...
Analysis\SpecialFunctions\Sqrt.lean
/- Copyright (c) 2021 Yury G. Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury G. Kudryashov -/ import Mathlib.Analysis.Calculus.ContDiff.Basic import Mathlib.Analysis.Calculus.Deriv.Pow /-! # Smoothness of `Real.sqrt` In this file we prove that `Real....
Analysis\SpecialFunctions\Stirling.lean
/- Copyright (c) 2022 Moritz Firsching. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Moritz Firsching, Fabian Kruse, Nikolas Kuhn -/ import Mathlib.Analysis.PSeries import Mathlib.Data.Real.Pi.Wallis import Mathlib.Tactic.AdaptationNote /-! # Stirling's formula Thi...
Analysis\SpecialFunctions\Complex\Analytic.lean
/- Copyright (c) 2024 Geoffrey Irving. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Geoffrey Irving -/ import Mathlib.Analysis.Analytic.Composition import Mathlib.Analysis.Analytic.Constructions import Mathlib.Analysis.Complex.CauchyIntegral import Mathlib.Analysis.S...
Analysis\SpecialFunctions\Complex\Arctan.lean
/- Copyright (c) 2024 Jeremy Tan. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jeremy Tan -/ import Mathlib.Analysis.SpecialFunctions.Complex.LogBounds /-! # Complex arctangent This file defines the complex arctangent `Complex.arctan` as $$\arctan z = -\frac i2 \lo...
Analysis\SpecialFunctions\Complex\Arg.lean
/- Copyright (c) 2018 Chris Hughes. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Chris Hughes, Abhimanyu Pallavi Sudhir, Jean Lo, Calle Sönne, Benjamin Davidson -/ import Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle import Mathlib.Analysis.SpecialFunctions.T...
Analysis\SpecialFunctions\Complex\Circle.lean
/- Copyright (c) 2021 Yury G. Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury G. Kudryashov -/ import Mathlib.Analysis.Complex.Circle import Mathlib.Analysis.SpecialFunctions.Complex.Log /-! # Maps on the unit circle In this file we prove some basic l...
Analysis\SpecialFunctions\Complex\CircleAddChar.lean
/- Copyright (c) 2024 David Loeffler. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: David Loeffler -/ import Mathlib.Analysis.SpecialFunctions.Complex.Circle import Mathlib.NumberTheory.LegendreSymbol.AddCharacter /-! # Additive characters valued in the unit circle ...
Analysis\SpecialFunctions\Complex\Log.lean
/- Copyright (c) 2018 Chris Hughes. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Chris Hughes, Abhimanyu Pallavi Sudhir, Jean Lo, Calle Sönne, Benjamin Davidson -/ import Mathlib.Analysis.SpecialFunctions.Complex.Arg import Mathlib.Analysis.SpecialFunctions.Log.Basic...
Analysis\SpecialFunctions\Complex\LogBounds.lean
/- Copyright (c) 2023 Michael Stoll. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Michael Stoll -/ import Mathlib.Analysis.Complex.Convex import Mathlib.Analysis.SpecialFunctions.Integrals import Mathlib.Analysis.Calculus.Deriv.Shift /-! # Estimates for the complex ...
Analysis\SpecialFunctions\Complex\LogDeriv.lean
/- Copyright (c) 2018 Chris Hughes. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Chris Hughes, Abhimanyu Pallavi Sudhir, Jean Lo, Calle Sönne, Benjamin Davidson -/ import Mathlib.Analysis.Calculus.InverseFunctionTheorem.Deriv import Mathlib.Analysis.Calculus.LogDeriv...
Analysis\SpecialFunctions\ContinuousFunctionalCalculus\ExpLog.lean
/- Copyright (c) 2024 Frédéric Dupuis. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Frédéric Dupuis -/ import Mathlib.Analysis.Normed.Algebra.Spectrum import Mathlib.Analysis.SpecialFunctions.Exponential import Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalcu...
Analysis\SpecialFunctions\Gamma\Basic.lean
/- Copyright (c) 2022 David Loeffler. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: David Loeffler -/ import Mathlib.MeasureTheory.Integral.ExpDecay import Mathlib.Analysis.MellinTransform /-! # The Gamma function This file defines the `Γ` function (of a real or com...
Analysis\SpecialFunctions\Gamma\Beta.lean
/- Copyright (c) 2023 David Loeffler. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: David Loeffler -/ import Mathlib.Analysis.Convolution import Mathlib.Analysis.SpecialFunctions.Trigonometric.EulerSineProd import Mathlib.Analysis.SpecialFunctions.Gamma.BohrMollerup i...
Analysis\SpecialFunctions\Gamma\BohrMollerup.lean
/- Copyright (c) 2023 David Loeffler. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: David Loeffler -/ import Mathlib.Analysis.SpecialFunctions.Gaussian.GaussianIntegral /-! # Convexity properties of the Gamma function In this file, we prove that `Gamma` and `log ∘ G...
Analysis\SpecialFunctions\Gamma\Deligne.lean
/- Copyright (c) 2024 David Loeffler. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: David Loeffler -/ import Mathlib.Analysis.SpecialFunctions.Gamma.Beta /-! # Deligne's archimedean Gamma-factors In the theory of L-series one frequently encounters the following fun...
Analysis\SpecialFunctions\Gaussian\FourierTransform.lean
/- Copyright (c) 2022 Sébastien Gouëzel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sébastien Gouëzel -/ import Mathlib.Analysis.SpecialFunctions.Gaussian.GaussianIntegral import Mathlib.Analysis.Complex.CauchyIntegral import Mathlib.MeasureTheory.Integral.Pi impor...
Analysis\SpecialFunctions\Gaussian\GaussianIntegral.lean
/- Copyright (c) 2022 Sébastien Gouëzel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sébastien Gouëzel -/ import Mathlib.Analysis.SpecialFunctions.Gamma.Basic import Mathlib.Analysis.SpecialFunctions.PolarCoord import Mathlib.Analysis.Convex.Complex /-! # Gaussian ...
Analysis\SpecialFunctions\Gaussian\PoissonSummation.lean
/- Copyright (c) 2023 David Loeffler. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: David Loeffler -/ import Mathlib.Analysis.SpecialFunctions.Gaussian.FourierTransform import Mathlib.Analysis.Fourier.PoissonSummation /-! # Poisson summation applied to the Gaussian ...
Analysis\SpecialFunctions\Log\Base.lean
/- Copyright (c) 2022 Bolton Bailey. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Bolton Bailey, Chris Hughes, Abhimanyu Pallavi Sudhir, Jean Lo, Calle Sönne -/ import Mathlib.Analysis.SpecialFunctions.Pow.Real import Mathlib.Data.Int.Log /-! # Real logarithm base `...
Analysis\SpecialFunctions\Log\Basic.lean
/- Copyright (c) 2018 Chris Hughes. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Chris Hughes, Abhimanyu Pallavi Sudhir, Jean Lo, Calle Sönne -/ import Mathlib.Analysis.SpecialFunctions.Exp import Mathlib.Data.Nat.Factorization.Defs import Mathlib.Analysis.NormedSpac...
Analysis\SpecialFunctions\Log\Deriv.lean
/- Copyright (c) 2018 Chris Hughes. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Chris Hughes, Abhimanyu Pallavi Sudhir, Jean Lo, Calle Sönne -/ import Mathlib.Analysis.Calculus.Deriv.Pow import Mathlib.Analysis.Calculus.LogDeriv import Mathlib.Analysis.SpecialFuncti...
Analysis\SpecialFunctions\Log\ENNRealLog.lean
/- Copyright (c) 2024 Damien Thomine. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Damien Thomine, Pietro Monticone, Rémy Degenne, Lorenzo Luccioli -/ import Mathlib.Data.Real.EReal import Mathlib.Analysis.SpecialFunctions.Pow.NNReal /-! # Extended Nonnegative Real ...
Analysis\SpecialFunctions\Log\ENNRealLogExp.lean
/- Copyright (c) 2024 Rémy Degenne. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Damien Thomine, Pietro Monticone, Rémy Degenne, Lorenzo Luccioli -/ import Mathlib.Analysis.SpecialFunctions.Log.ERealExp import Mathlib.Analysis.SpecialFunctions.Log.ENNRealLog import M...
Analysis\SpecialFunctions\Log\ERealExp.lean
/- Copyright (c) 2024 Rémy Degenne. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Pietro Monticone, Rémy Degenne, Lorenzo Luccioli -/ import Mathlib.Data.Complex.Exponential import Mathlib.Data.Real.EReal /-! # Extended Nonnegative Real Exponential We define `exp` a...
Analysis\SpecialFunctions\Log\Monotone.lean
/- Copyright (c) 2021 Bolton Bailey. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Bolton Bailey -/ import Mathlib.Analysis.SpecialFunctions.Pow.Real /-! # Logarithm Tonality In this file we describe the tonality of the logarithm function when multiplied by function...
Analysis\SpecialFunctions\Log\NegMulLog.lean
/- Copyright (c) 2023 Rémy Degenne. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Rémy Degenne -/ import Mathlib.Analysis.SpecialFunctions.Log.Deriv import Mathlib.Analysis.SpecialFunctions.Pow.Asymptotics import Mathlib.Analysis.Convex.Deriv /-! # The function `x ↦ ...
Analysis\SpecialFunctions\Pow\Asymptotics.lean
/- Copyright (c) 2018 Chris Hughes. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Chris Hughes, Abhimanyu Pallavi Sudhir, Jean Lo, Calle Sönne, Sébastien Gouëzel, Rémy Degenne, David Loeffler -/ import Mathlib.Analysis.SpecialFunctions.Pow.NNReal /-! # Limits and a...
Analysis\SpecialFunctions\Pow\Complex.lean
/- Copyright (c) 2018 Chris Hughes. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Chris Hughes, Abhimanyu Pallavi Sudhir, Jean Lo, Calle Sönne, Sébastien Gouëzel, Rémy Degenne, David Loeffler -/ import Mathlib.Analysis.SpecialFunctions.Complex.Log /-! # Power funct...
Analysis\SpecialFunctions\Pow\Continuity.lean
/- Copyright (c) 2018 Chris Hughes. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Chris Hughes, Abhimanyu Pallavi Sudhir, Jean Lo, Calle Sönne, Sébastien Gouëzel, Rémy Degenne, David Loeffler -/ import Mathlib.Analysis.SpecialFunctions.Pow.Asymptotics /-! # Continu...
Analysis\SpecialFunctions\Pow\Deriv.lean
/- Copyright (c) 2018 Chris Hughes. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Chris Hughes, Abhimanyu Pallavi Sudhir, Jean Lo, Calle Sönne, Sébastien Gouëzel, Rémy Degenne -/ import Mathlib.Analysis.SpecialFunctions.Pow.Continuity import Mathlib.Analysis.Special...
Analysis\SpecialFunctions\Pow\Integral.lean
/- Copyright (c) 2022 Kalle Kytölä. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kalle Kytölä -/ import Mathlib.Analysis.SpecialFunctions.Integrals import Mathlib.MeasureTheory.Integral.Layercake /-! # The integral of the real power of a nonnegative function In thi...
Analysis\SpecialFunctions\Pow\NNReal.lean
/- Copyright (c) 2018 Chris Hughes. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Chris Hughes, Abhimanyu Pallavi Sudhir, Jean Lo, Calle Sönne, Sébastien Gouëzel, Rémy Degenne, David Loeffler -/ import Mathlib.Analysis.SpecialFunctions.Pow.Real /-! # Power function...
Analysis\SpecialFunctions\Pow\Real.lean
/- Copyright (c) 2018 Chris Hughes. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Chris Hughes, Abhimanyu Pallavi Sudhir, Jean Lo, Calle Sönne, Sébastien Gouëzel, Rémy Degenne, David Loeffler -/ import Mathlib.Analysis.SpecialFunctions.Pow.Complex import Qq /-! # P...