Convergence and Gibbs phenomenon for double Fourier-Walsh series of functions of bounded harmonic variation (Q1921490)

Among others, the following theorem is proved: Theorem 3. If \(f(x,y)\) is of bounded harmonic variation on the unit square \([0,1]^2\) and continuous on a compact set \(K\subset[0,1]^2\), then the rectangular partial sums of the double Walsh-Fourier expansion of \(f\) converge uniformly on \(K\). The occurrence of the Gibbs phenomenon for double Walsh-Fourier series is also presented.