Theorems · Theorem · harmonic analysis

BoundedContinuousFunction.char_add_eq_mul

∀ {V : Type u_1} {W : Type u_2} [inst : AddCommGroup V] [inst_1 : Module ℝ V] [inst_2 : TopologicalSpace V]
  [inst_3 : AddCommGroup W] [inst_4 : Module ℝ W] [inst_5 : TopologicalSpace W] {e : AddChar ℝ Circle}
  {L : V →ₗ[ℝ] W →ₗ[ℝ] ℝ} {he : Continuous ⇑e} {hL : Continuous fun p => (L p.1) p.2} (x y : W),
  BoundedContinuousFunction.char he hL (x + y) =
    BoundedContinuousFunction.char he hL x * BoundedContinuousFunction.char he hL y

Defined in

Mathlib.Analysis.Fourier.BoundedContinuousFunctionChar

Cited by

1 results in Mathlib

Foundations

Depth 166 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommGroupModuleTopologicalSpaceAddCommGroupModuleTopologicalSpace