Equiconvergence of expansions in multiple trigonometric Fourier series and Fourier integral with "Jk-lacunary sequences of rectangular partial sums"

Igor L. Bloshanskii; Denis A. Grafov

doi:10.12697/ACUTM.2014.18.08

Igor L. Bloshanskii Department of Mathematical Analysis and Geometry, Moscow State Regional University, 105005 Moscow, 10a Radio Street
Denis A. Grafov Department of Mathematical Analysis and Geometry, Moscow State Regional University, 105005 Moscow, 10a Radio Street

DOI: https://doi.org/10.12697/ACUTM.2014.18.08

Keywords: multiple trigonometric Fourier series, multiple Fourier integral, convergence almost everywhere, lacunary sequence

Abstract

We give a review of recent results on equiconvergence of expansions in multiple trigonometric Fourier series and Fourier integral in the case of summation over rectangles.

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