Convergence of multiple Fourier series of functions of bounded generalized variation

TL;DR

This paper introduces a new concept of $ ext{Lambda}$-variation for multivariable functions and explores its relationship with the convergence properties of multidimensional Fourier series.

Contribution

It proposes a novel $ ext{Lambda}$-variation framework for functions of multiple variables and analyzes its impact on Fourier series convergence.

Findings

$ ext{Lambda}$-variation influences Fourier series convergence

New criteria for convergence based on $ ext{Lambda}$-variation

Enhanced understanding of multivariable Fourier analysis

Abstract

The paper introduces a new concept of $\Lambda $-variation of multivariable functions and investigates its connection with the convergence of multidimensional Fourier series