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Russian Mathematical Surveys, 1976, Volume 31, Issue 6, Pages 29–86
DOI: https://doi.org/10.1070/RM1976v031n06ABEH001575 (Mi rm3993) 		 
This article is cited in 47 scientific papers (total in 48 papers)

Convergence problems of multiple trigonometric series and spectral decompositions. I

Sh. A. Alimov, V. A. Il'in, E. M. Nikishin
English version PDF (2902 kB) Citations (48)
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DOI: https://doi.org/10.1070/RM1976v031n06ABEH001575
Abstract: This article is a survey of the present state of convergence problems of multiple trigonometric series and spectral decompositions corresponding to self-adjoint elliptic differential operators. Particular attention is paid to questions of localization, uniform convergence, convergence in mean, convergence almost everywhere, and also of absolute convergence. In some cases short sketches of proofs of important propositions are given. This applies mostly to Chapter III, which contains a large number of new proofs of various propositions connected with convergence problems of spectral decompositions.
In addition, the article mentions unsolved questions and formulates many new problems
Received: 11.02.1975
Russian version:
Uspekhi Matematicheskikh Nauk, 1976, Volume 31, Issue 6(192), Pages 28–83
Bibliographic databases:
Document Type: Article
UDC: 517.4+517.5
MSC: 42A20, 42A32, 42A24
Language: English
Original paper language: Russian
Citation: Sh. A. Alimov, V. A. Il'in, E. M. Nikishin, “Convergence problems of multiple trigonometric series and spectral decompositions. I”, Uspekhi Mat. Nauk, 31:6(192) (1976), 28–83; Russian Math. Surveys, 31:6 (1976), 29–86
Citation in format AMSBIB
\Bibitem{AliIliNik76}
\by Sh.~A.~Alimov, V.~A.~Il'in, E.~M.~Nikishin
\paper Convergence problems of multiple trigonometric series and spectral decompositions.~I
\jour Uspekhi Mat. Nauk
\yr 1976
\vol 31
\issue 6(192)
\pages 28--83
\mathnet{http://mi.mathnet.ru/rm3993}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=461028}
\zmath{https://zbmath.org/?q=an:0345.42005|0367.42008}
\transl
\jour Russian Math. Surveys
\yr 1976
\vol 31
\issue 6
\pages 29--86
\crossref{https://doi.org/10.1070/RM1976v031n06ABEH001575}
Linking options:
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  • https://doi.org/10.1070/RM1976v031n06ABEH001575
  • https://www.mathnet.ru/eng/rm/v31/i6/p28
    Cycle of papers
    This publication is cited in the following 48 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Успехи математических наук Russian Mathematical Surveys
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    Abstract page:1223
    Russian version PDF:565
    English version PDF:39
    References:97
    First page:2
     
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