What question did this study set out to answer?

The central aim is to analyze the convergence properties of multi-dimensional Fourier series within Sobolev spaces.

April 24, 2026Mathematical Methods in the Applied Sciences0 citations

Convergence Analysis of The Multi‐Dimensional Fourier Series in Sobolev Spaces by Using Hausdorff Matrices

Key Points

The central aim is to analyze the convergence properties of multi-dimensional Fourier series within Sobolev spaces.
Examined double Fourier series representation for functions
Extended analysis to N-dimensional Fourier series
Applied Hausdorff matrices in the convergence assessment
Identified conditions under which convergence is achieved
Demonstrated the utility of Hausdorff matrices in the analysis
Extended results applicable to N-dimensional cases

Abstract

ABSTRACT In this work, we delve into the convergence analysis concerning a function represented by double Fourier series within Sobolev spaces. Further, we expand our convergence analysis for N‐dimensional Fourier series.

问 AI

Bookmark

View Full Paper