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Mathematics of the USSR-Izvestiya, 1972, Volume 6, Issue 4, Pages 788–806
DOI: https://doi.org/10.1070/IM1972v006n04ABEH001901 (Mi im2335) 		 
This article is cited in 13 scientific papers (total in 14 papers)

A resonance theorem and series in eigenfunctions of the Laplacian

E. M. Nikishin
English version PDF (611 kB) Citations (14)
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DOI: https://doi.org/10.1070/IM1972v006n04ABEH001901
Abstract: By means of a resonance theorem we will establish the existence of functions in $L_p(\Omega)$ (where $\Omega$ is an $N$-dimensional region) whose expansion in eigenfunctions of the Laplacian is not Riesz-summable of order $a<N\bigl(\frac1p-\frac12\bigr)-\frac12$ if $1\leqslant p<\frac{2N}{N+1}$.
Received: 07.12.1970
Russian version:
Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya, 1972, Volume 36, Issue 4, Pages 795–813
Bibliographic databases:
UDC: 517.5
MSC: Primary 35P10, 40G99; Secondary 42A60
Language: English
Original paper language: Russian
Citation: E. M. Nikishin, “A resonance theorem and series in eigenfunctions of the Laplacian”, Izv. Akad. Nauk SSSR Ser. Mat., 36:4 (1972), 795–813; Math. USSR-Izv., 6:4 (1972), 788–806
Citation in format AMSBIB
\Bibitem{Nik72}
\by E.~M.~Nikishin
\paper A~resonance theorem and series in eigenfunctions of the Laplacian
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1972
\vol 36
\issue 4
\pages 795--813
\mathnet{http://mi.mathnet.ru/im2335}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=343091}
\zmath{https://zbmath.org/?q=an:0258.42018}
\transl
\jour Math. USSR-Izv.
\yr 1972
\vol 6
\issue 4
\pages 788--806
\crossref{https://doi.org/10.1070/IM1972v006n04ABEH001901}
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  • https://www.mathnet.ru/eng/im/v36/i4/p795
    Erratum
    This publication is cited in the following 14 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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    Abstract page:539
    Russian version PDF:151
    English version PDF:211
    References:48
    First page:1
     
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