Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika
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Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika, 2016, Number 2, Pages 18–24 (Mi vmumm131)  
Mathematics

The condition of almost everywhere convergence for a functional series with a weak analogue of the orthonormality property

V. V. Galatenko, T. P. Lukashenko, V. A. Sadovnichii

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
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Abstract: The almost everywhere convergence condition similar to the Menchoff–Rademacher condition is obtained for functional series with some weak analogue of the orthogonality property. As a corollary, the results of almost everywhere convergence of series with respect to Riesz systems, Hilbert and Bessel systems, and frames are obtained.
Key words: almost everywhere convergence, Menchoff–Rademacher condition, Riesz systems, Hilbert systems, Bessel systems, frames.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation НШ-7461.2016.1
Russian Foundation for Basic Research 14-01-00417
Received: 25.09.2015
English version:
Moscow University Mathematics Bulletin, 2016, Volume 71, Issue 2, Pages 61–67
DOI: https://doi.org/10.3103/S0027132216020030
Bibliographic databases:
Document Type: Article
UDC: 517.518
Language: Russian
Citation: V. V. Galatenko, T. P. Lukashenko, V. A. Sadovnichii, “The condition of almost everywhere convergence for a functional series with a weak analogue of the orthonormality property”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2016, no. 2, 18–24; Moscow University Mathematics Bulletin, 71:2 (2016), 61–67
Citation in format AMSBIB
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