Equiconvergence of expansion in a triple trigonometric series and Fourier integral of continuous functions with a certain modulus of continuity / D. A. Grafov. // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2015. № 1. P. 25-33 [Moscow Univ. Math. Bulletin. Vol. 72, N 2, 2017. P. 24-32].

We study the problem of equiconvergence on \mathbb T^3=[-\pi, \pi)^3 for expansions in a triple trigonometric Fourier series and a Fourier integral of continuous functions with a certain modulus of continuity in the case of a "lacunary sequence of partial sums".

Key words: multiple trigonometric Fourier series, multiple Fourier integrals, convergence almost everywhere, lacunary sequence.

№ 1/2015