`BookProof.majoranaFourier_symm` (Θ : (Lp F 2 (volume : Measure E)) ≃ₗᵢ[ℝ] P) : (majoranaFourier E F Θ).symm = conjugateₗᵢ Θ (pauliFourier E F).symm

Proved

BookProof.majoranaFourier_symm

by leonardopedro · Oct 7, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterA4.

BookProof.majoranaFourier_symm (Θ : (Lp F 2 (volume : Measure E)) ≃ₗᵢ[ℝ] P) : (majoranaFourier E F Θ).symm = conjugateₗᵢ Θ (pauliFourier E F).symm

Formalization note: Lean 4 identifier BookProof.majoranaFourier_symm.

Preamble

-- Generated from ChapterA4.lean — theorem BookProof.majoranaFourier_symm
import Mathlib
import Definitions.Def_ChapterA4
open BookProof



open MeasureTheory




variable {R E E' : Type*} [Semiring R]
    [SeminormedAddCommGroup E] [SeminormedAddCommGroup E'] [Module R E] [Module R E']

variable (E F : Type*) [NormedAddCommGroup E] [MeasurableSpace E] [BorelSpace E]
    [NormedAddCommGroup F] [InnerProductSpace ℂ F] [CompleteSpace F]
    [InnerProductSpace ℝ E] [FiniteDimensional ℝ E]
variable {P : Type*} [NormedAddCommGroup P] [InnerProductSpace ℝ P]

Formal statement

theorem BookProof.majoranaFourier_symm
    (Θ : (Lp F 2 (volume : Measure E)) ≃ₗᵢ[ℝ] P) :
    (majoranaFourier E F Θ).symm = conjugateₗᵢ Θ (pauliFourier E F).symm := by sorry

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