Theorems · Definition

FourierTransform.fourierCLE

(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] →
                  [FourierAdd E F] →
                    [FourierSMul R E F] →
                      [inst_8 : FourierTransformInv F E] →
                        [FourierPair E F] →
                          [FourierInvPair F E] →
                            [inst_11 : TopologicalSpace E] →
                              [inst_12 : TopologicalSpace F] →
                                [ContinuousFourier E F] → [ContinuousFourierInv F E] → E ≃L[R] F

The Fourier transform as a continuous linear equivalence.

Defined in

Mathlib.Analysis.Fourier.Notation

Cited by

4 results in Mathlib

Foundations

Depth 23 from the axioms · uses propext, Quot.sound

Assumes

SemiringAddCommMonoidAddCommMonoidModuleModuleFourierTransformFourierAddFourierSMulFourierTransformInvFourierPairFourierInvPairTopologicalSpaceTopologicalSpaceContinuousFourierContinuousFourierInv