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Izv. Akad. Nauk SSSR Ser. Mat., 1984, Volume 48, Issue 4, Pages 833–853 (Mi izv1493)  

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

Decomposition of an analytic function into a sum of periodic functions

A. M. Sedletskii


Abstract: Let $D$ be a convex polygon in $\mathbf C$ with vertices $a_1,…,a_m$, $m$ odd, and let $P_k$ be the half-plane bounded by an extension of the side $(a_k,a_{k+1})$ and containing $D$. A necessary and sufficient condition is found for a function analytic in $D$ and continuous on $\overline D$ to split into a sum of functions $f_k(z)$, $k=1,…,m$, where $f_k(z)$ is analytic in $P_k$, continuous in $\overline P_k$ and periodic with period $a_{k+1}-a_k$.
Bibliography: 11 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1985, 25:1, 163–181

Bibliographic databases:

UDC: 517.5
MSC: Primary 30B50; Secondary 30D40, 42A50, 46E15, 40G05
Received: 01.06.1982

Citation: A. M. Sedletskii, “Decomposition of an analytic function into a sum of periodic functions”, Izv. Akad. Nauk SSSR Ser. Mat., 48:4 (1984), 833–853; Math. USSR-Izv., 25:1 (1985), 163–181

Citation in format AMSBIB
\Bibitem{Sed84}
\by A.~M.~Sedletskii
\paper Decomposition of an analytic function into a~sum of periodic functions
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1984
\vol 48
\issue 4
\pages 833--853
\mathnet{http://mi.mathnet.ru/izv1493}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=755959}
\zmath{https://zbmath.org/?q=an:0581.30002}
\transl
\jour Math. USSR-Izv.
\yr 1985
\vol 25
\issue 1
\pages 163--181
\crossref{https://doi.org/10.1070/IM1985v025n01ABEH001274}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. M. Sedletskii, “Projection from the spaces $E^p$ on a convex polygon onto subspaces of periodic functions”, Math. USSR-Izv., 33:2 (1989), 373–390  mathnet  crossref  mathscinet  zmath
    2. Takanao Negishi, “On periodic decomposition of entire functions of several variables”, Aequat. Math, 2014  crossref
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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