A Fourier Inversion Theorem for Normal Functions

2024/03/28 by Tristram de Piro, de Piro, Tristram
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Algebraic and Geometric Analysis #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · pdf · doi:10.48550/arxiv.2403.19761

openalex publication_date 2024/03/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove an inversion theorem for the Fourier transform defined for normal functions, in the case when such functions are of moderate decrease, and in dimensions 2 and 3. This improves on Carleson's general almost everywhere convergence result for square integrable functions to everywhere convergence, in the special case of normal functions of moderate decrease. The class of normal functions appear in Physics and the everywhere convergence is important for further analysis of wave equations and no radiation properties of electromagnetic fields.

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