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