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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2022, Volume 207, Pages 61–67
DOI: https://doi.org/10.36535/0233-6723-2022-207-61-67 (Mi into980) 		 
Equiconvergence and equisummability almost everywhere of a multiple orthogonal series for various types of convergence

B. V. Konoplev

Saratov State University
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DOI: https://doi.org/10.36535/0233-6723-2022-207-61-67
Abstract: In this paper, we obtain coefficient conditions that guarantee the equiconvergence and Cesaro equisummability almost everywhere of a multiple orthogonal series summed over two different systems of nested sets covering an integer lattice of the arithmetic space.
Keywords: multiple orthogonal series, partial sum, Cesaro mean, convergence almost everywhere, summability almost everywhere, star body, homothety, multiple trigonomrtric series.
Document Type: Article
UDC: 517.521.5, 517.521.8
MSC: 35L20, 35P10
Language: Russian
Citation: B. V. Konoplev, “Equiconvergence and equisummability almost everywhere of a multiple orthogonal series for various types of convergence”, Proceedings of the Voronezh International Winter Mathematical School "Modern Methods of Function Theory and Related Problems", Voronezh, January 28 - February 2, 2021, Part 2, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 207, VINITI, Moscow, 2022, 61–67
Citation in format AMSBIB
\Bibitem{Kon22}
\by B.~V.~Konoplev
\paper Equiconvergence and equisummability almost everywhere of a multiple orthogonal series for various types of convergence
\inbook Proceedings of the Voronezh International Winter Mathematical School "Modern Methods of Function Theory and Related Problems", Voronezh, January 28 - February 2, 2021, Part 2
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2022
\vol 207
\pages 61--67
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into980}
\crossref{https://doi.org/10.36535/0233-6723-2022-207-61-67}
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