Prove2Me

`BookProof.NsScalarFourier.nsScalarFourier_apply` (g : Lp ℂ 2 ((volume : Measure V).prod (volume : Measure W))) : nsScalarFourier V W g = curryLI (nsPartialFourier V W (curryLI.sym

Proved
BookProof.NsScalarFourier.nsScalarFourier_apply

by leonardopedro · Oct 10, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterNsScalarFourier.

BookProof.NsScalarFourier.nsScalarFourier_apply (g : Lp ℂ 2 ((volume : Measure V).prod (volume : Measure W))) : nsScalarFourier V W g = curryLI (nsPartialFourier V W (curryLI.symm g))

Formalization note: Lean 4 identifier BookProof.NsScalarFourier.nsScalarFourier_apply.

Preamble
-- Generated from ChapterNsScalarFourier.lean — theorem BookProof.NsScalarFourier.nsScalarFourier_apply
import Definitions.Def_ChapterNsScalarVectorCurry
import Mathlib
import Definitions.Def_ChapterNsScalarFourier
import Definitions.Def_ChapterNsPartialFourier
open BookProof.NsPartialFourier
open BookProof.NsScalarFourier


open MeasureTheory


open BookProof.NsPartialFourier BookProof.NsScalarVectorCurry

noncomputable section

variable {V : Type*} [NormedAddCommGroup V] [InnerProductSpace ℝ V] [FiniteDimensional ℝ V]
  [MeasurableSpace V] [BorelSpace V]
variable {W : Type*} [NormedAddCommGroup W] [InnerProductSpace ℝ W] [FiniteDimensional ℝ W]
  [MeasurableSpace W] [BorelSpace W]

variable (V W) in
Formal statement
theorem BookProof.NsScalarFourier.nsScalarFourier_apply (g : Lp ℂ 2 ((volume : Measure V).prod (volume : Measure W))) :
    nsScalarFourier V W g = curryLI (nsPartialFourier V W (curryLI.symm g)) := by sorry

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