Theorems · Theorem · harmonic analysis

VectorFourier.hasFDerivAt_fourierChar_smul

∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℂ E] {V : Type u_2} {W : Type u_3}
  [inst_2 : NormedAddCommGroup V] [inst_3 : NormedSpace ℝ V] [inst_4 : NormedAddCommGroup W] [inst_5 : NormedSpace ℝ W]
  (L : V →L[ℝ] W →L[ℝ] ℝ) (f : V → E) (v : V) (w : W),
  HasFDerivAt (fun w' => Real.fourierChar (-(L v) w') • f v)
    (Real.fourierChar (-(L v) w) • VectorFourier.fourierSMulRight L f v) w

The w-derivative of the Fourier transform integrand.

Defined in

Mathlib.Analysis.Fourier.FourierTransformDeriv

Cited by

1 results in Mathlib

Foundations

Depth 207 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace