On the divergence of triangular and eccentrical spherical sums of double Fourier series

TL;DR

This paper demonstrates that certain double Fourier series sums, specifically triangular and eccentrical spherical sums, can diverge almost everywhere for some continuous functions on the torus.

Contribution

It proves divergence of triangular and eccentrical spherical sums for continuous functions, extending understanding of convergence behavior in double Fourier series.

Findings

Triangular sums diverge almost everywhere for some continuous functions.

Eccentrical spherical sums also diverge almost everywhere.

Provides new divergence results in Fourier analysis.

Abstract

We construct a continuous function on the torus with almost everywhere divergence triangular sums of double Fourier series. An analogous theorem we also prove for eccentrical spherical sums.