Theorems · Theorem · harmonic analysis

BoundedContinuousFunction.star_mem_range_charAlgHom

∀ {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 : BoundedContinuousFunction V ℂ},
  x ∈ (BoundedContinuousFunction.charAlgHom he hL).range → star x ∈ (BoundedContinuousFunction.charAlgHom he hL).range

The family of ℂ-linear combinations of char he hL w, w : W, is closed under star.

Defined in

Mathlib.Analysis.Fourier.BoundedContinuousFunctionChar

Cited by

0 results in Mathlib

Foundations

Depth 172 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommGroupModuleTopologicalSpaceAddCommGroupModuleTopologicalSpace