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Mat. Zametki, 1976, Volume 19, Issue 3, Pages 435–448 (Mi mz7762)  

Absolute convergence of Fourier series in eigenfunctions of an elliptic operator

V. S. Serov

M. V. Lomonosov Moscow State University

Abstract: In this article we investigate absolute convergence of Fourier series in eigenfunctions of an $m$-th order elliptic operator on functions in the Besov class $B_{2,\theta}^{N/2}$. We show that in terms of Besov classes the theorem of Peetre on absolute convergence of series in eigenfunctions in the class $B_{2,1}^{N/2}$ is best possible. We construct a function in $B_{2,\theta}^{N/2}$ whose Fourier series is absolutely divergent at any preassigned point.

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English version:
Mathematical Notes, 1976, 19:3, 266–274

Bibliographic databases:

UDC: 517.4
Received: 20.02.1975

Citation: V. S. Serov, “Absolute convergence of Fourier series in eigenfunctions of an elliptic operator”, Mat. Zametki, 19:3 (1976), 435–448; Math. Notes, 19:3 (1976), 266–274

Citation in format AMSBIB
\Bibitem{Ser76}
\by V.~S.~Serov
\paper Absolute convergence of Fourier series in eigenfunctions of an elliptic operator
\jour Mat. Zametki
\yr 1976
\vol 19
\issue 3
\pages 435--448
\mathnet{http://mi.mathnet.ru/mz7762}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=425379}
\zmath{https://zbmath.org/?q=an:0338.35069|0331.35047}
\transl
\jour Math. Notes
\yr 1976
\vol 19
\issue 3
\pages 266--274
\crossref{https://doi.org/10.1007/BF01437862}


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