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Mat. Zametki, 1975, Volume 18, Issue 1, Pages 9–17 (Mi mz7619)  

This article is cited in 2 scientific papers (total in 2 papers)

Equiconvergence and equisummability of nonharmonic Fourier expansions with ordinary trigonometric series

A. M. Sedletskii

Moscow Power Engineering Institute

Abstract: Given $f\in L(-\pi,\pi)$, we consider its nonharmonic Fourier series $f(x)\sim\sum c_ne^{i\lambda}n^x$, where $\lambda_n$ are the roots of the entire function $L(z)=\int_{-\pi}^\pi e^{izt} d\sigma(T)$. We show that this series is equiconvergent, uniformly inside $(-\pi,\pi)$, and equisummable with the Fourier series of $f$ with respect to the trigonometric system if $\sigma'(t)=k(t)(\pi-|t|)^{-\alpha}$, $\alpha\in(0,1)$, $\operatorname{var}k<\infty$, $k(\pi-0)\ne0$, $k(-\pi+0)\ne0$.

Full text: PDF file (591 kB)

English version:
Mathematical Notes, 1975, 18:1, 586–591

Bibliographic databases:

UDC: 51?
Received: 29.05.1974

Citation: A. M. Sedletskii, “Equiconvergence and equisummability of nonharmonic Fourier expansions with ordinary trigonometric series”, Mat. Zametki, 18:1 (1975), 9–17; Math. Notes, 18:1 (1975), 586–591

Citation in format AMSBIB
\Bibitem{Sed75}
\by A.~M.~Sedletskii
\paper Equiconvergence and equisummability of nonharmonic Fourier expansions with ordinary trigonometric series
\jour Mat. Zametki
\yr 1975
\vol 18
\issue 1
\pages 9--17
\mathnet{http://mi.mathnet.ru/mz7619}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=385449}
\zmath{https://zbmath.org/?q=an:0313.42009}
\transl
\jour Math. Notes
\yr 1975
\vol 18
\issue 1
\pages 586--591
\crossref{https://doi.org/10.1007/BF01461135}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. M. Sedletskii, “Extension of convergence of quasipolynomials”, Math. USSR-Izv., 17:2 (1981), 353–368  mathnet  crossref  mathscinet  zmath  isi
    2. A. M. Sedletskii, “Biorthogonal expansions of functions in series of exponents on intervals of the real axis”, Russian Math. Surveys, 37:5 (1982), 57–108  mathnet  crossref  mathscinet  zmath  adsnasa  isi
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