Theorems · Theorem · harmonic analysis

Real.hasFDerivAt_fourierChar_neg_bilinear_left

∀ {V : Type u_1} {W : Type u_2} [inst : NormedAddCommGroup V] [inst_1 : NormedSpace ℝ V] [inst_2 : NormedAddCommGroup W]
  [inst_3 : NormedSpace ℝ W] (L : V →L[ℝ] W →L[ℝ] ℝ) (v : V) (w : W),
  HasFDerivAt (fun v => ↑(Real.fourierChar (-(L v) w)))
    ((-2 * ↑Real.pi * Complex.I * ↑(Real.fourierChar (-(L v) w))) • Complex.ofRealCLM ∘SL L.flip w) v

Defined in

Mathlib.Analysis.Fourier.FourierTransformDeriv

Cited by

2 results in Mathlib

Foundations

Depth 208 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace