`BookProof.ChapterSphericalPlancherel.sineKernelTransform_eq` (G : ℝ → ℂ) (p : ℝ) : sineKernelTransform G p = sineTransform G ((2 * π)⁻¹ * p)

Proved

BookProof.ChapterSphericalPlancherel.sineKernelTransform_eq

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSphericalPlancherel.

BookProof.ChapterSphericalPlancherel.sineKernelTransform_eq (G : ℝ → ℂ) (p : ℝ) : sineKernelTransform G p = sineTransform G ((2 * π)⁻¹ * p)

Formalization note: Lean 4 identifier BookProof.ChapterSphericalPlancherel.sineKernelTransform_eq.

Preamble

-- Generated from ChapterSphericalPlancherel.lean — theorem BookProof.ChapterSphericalPlancherel.sineKernelTransform_eq
import Definitions.Def_ChapterSphericalBessel
import Mathlib
import Definitions.Def_ChapterSphericalPlancherel
open BookProof.ChapterSphericalPlancherel



open MeasureTheory Set Real SchwartzMap
open scoped FourierTransform ContDiff
open BookProof.ChapterSphericalBessel

Formal statement

theorem BookProof.ChapterSphericalPlancherel.sineKernelTransform_eq (G : ℝ → ℂ) (p : ℝ) :
    sineKernelTransform G p = sineTransform G ((2 * π)⁻¹ * p) := by sorry

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