Theorems · Theorem · functional analysis

SchwartzMap.norm_fourier_toL2_eq

∀ {V : Type u_3} [inst : NormedAddCommGroup V] [inst_1 : InnerProductSpace ℝ V] [inst_2 : FiniteDimensional ℝ V]
  [inst_3 : MeasurableSpace V] [inst_4 : BorelSpace V] {H : Type u_4} [inst_5 : NormedAddCommGroup H]
  [inst_6 : InnerProductSpace ℂ H] [CompleteSpace H] (f : SchwartzMap V H),
  ‖(FourierTransform.fourier f).toLp 2 MeasureTheory.volume‖ = ‖f.toLp 2 MeasureTheory.volume‖

Defined in

Mathlib.Analysis.Distribution.SchwartzSpace.Fourier

Cited by

2 results in Mathlib

Foundations

Depth 306 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpaceFiniteDimensionalMeasurableSpaceBorelSpaceNormedAddCommGroupInnerProductSpaceCompleteSpace