Theorems · Theorem · functional analysis

SchwartzMap.fourierTransformCLE_symm_apply

Deprecated since 2026-01-06Use FourierTransform.fourierCLE_symm_apply instead.

∀ {R : Type u_5} {E : Type u_6} {F : Type u_7} [inst : Semiring R] [inst_1 : AddCommMonoid E] [inst_2 : AddCommMonoid F]
  [inst_3 : Module R E] [inst_4 : Module R F] [inst_5 : FourierTransform E F] [inst_6 : FourierAdd E F]
  [inst_7 : FourierSMul R E F] [inst_8 : FourierTransformInv F E] [inst_9 : FourierPair E F]
  [inst_10 : FourierInvPair F E] [inst_11 : TopologicalSpace E] [inst_12 : TopologicalSpace F]
  [inst_13 : ContinuousFourier E F] [inst_14 : ContinuousFourierInv F E] (f : F),
  (FourierTransform.fourierCLE R E).symm f = FourierTransformInv.fourierInv f

Alias of FourierTransform.fourierCLE_symm_apply.

Defined in

Mathlib.Analysis.Distribution.SchwartzSpace.Fourier

Cited by

0 results in Mathlib

Foundations

Depth 29 from the axioms · uses propext, Quot.sound

Assumes

SemiringAddCommMonoidAddCommMonoidModuleModuleFourierTransformFourierAddFourierSMulFourierTransformInvFourierPairFourierInvPairTopologicalSpaceTopologicalSpaceContinuousFourierContinuousFourierInv