Inversin of double Fourier integral of non-Lebesgue integrable bounded variation functions

TL;DR

This paper establishes pointwise convergence of truncated double Fourier integrals for non-Lebesgue integrable bounded variation functions, extending classical Fourier analysis results to a broader class of functions.

Contribution

It proves the Dirichlet-Jordan theorem for non-Lebesgue integrable functions, a novel extension beyond previous Lebesgue-focused studies.

Findings

Proves pointwise convergence of double Fourier integrals for non-Lebesgue functions

Extends Dirichlet-Jordan theorem to non-Lebesgue integrable functions

Addresses a gap in Fourier analysis literature

Abstract

This work proves pointwise convergence of the truncated Fourier double integral of non-Lebesgue integrable bounded variation functions. This leads to the Dirichlet-Jordan theorem proof for non-Lebesgue integrable functions, which has not been sufficiently studied. Note that recent contributions regarding this subject consider Lebesgue integrable functions, [F. Moricz, 2015], [B. Ghodadra-V. Fuulop, 2016].