Equiconvergence of expansions in multiple Fourier series and in fourier integrals with “lacunary sequences of partial sums”
- Authors: Bloshanskii I.L.1, Grafov D.A.1
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Affiliations:
- Moscow State Regional University
- Issue: Vol 99, No 1-2 (2016)
- Pages: 196-209
- Section: Article
- URL: https://journals.rcsi.science/0001-4346/article/view/149084
- DOI: https://doi.org/10.1134/S0001434616010235
- ID: 149084
Cite item
Abstract
We investigate the equiconvergence on TN = [−π, π)N of expansions in multiple trigonometric Fourier series and in the Fourier integrals of functions f ∈ Lp(TN) and g ∈ Lp(RN), p > 1, N ≥ 3, g(x) = f(x) on TN, in the case where the “partial sums” of these expansions, i.e., Sn(x; f) and Jα(x; g), respectively, have “numbers” n ∈ ZN and α ∈ RN (nj = [αj], j = 1,..., N, [t] is the integral part of t ∈ R1) containing N − 1 components which are elements of “lacunary sequences.”
About the authors
I. L. Bloshanskii
Moscow State Regional University
Author for correspondence.
Email: ig.bloshn@gmail.com
Russian Federation, Moscow
D. A. Grafov
Moscow State Regional University
Email: ig.bloshn@gmail.com
Russian Federation, Moscow