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Izv. Akad. Nauk SSSR Ser. Mat., 1978, Volume 42, Issue 5, Pages 1101–1119 (Mi izv1928)  

This article is cited in 4 scientific papers (total in 4 papers)

Bases of exponential functions in the spaces $E^p$ on convex polygons

A. M. Sedletskii


Abstract: Let $D$ be a convex polygon in the complex plane; let $a_1,a_2,…,a_m$ $(m\geq 3)$ be its vertices, numbered in the order of a circuit around $D$ in the positive direction; let $\varphi_k=\arg(a_{k+1}-a_k)-\pi/2$; and let $2l_k$ be the length of the edge $a_k$, $a_{k+1}$. Let $\Lambda=\Lambda_1\cup\Lambda_2\cup…\cup\Lambda_m$, where
$$ \Lambda_k=\{l^{-1}_ke^{-i\varphi_k}(\pi n+\frac\pi2+\alpha_k+\varepsilon_{kn})\}_{n=0}^{+\infty},\quad k=1,2,…,m. $$
If $\alpha_1+…+\alpha_m=0$ and $\{\varepsilon_{kn}\}\in l^2$ for $p\geqslant2$ and $\{\varepsilon_{kn}\}\in l^p$ for $1<p\leqslant2$, $ k=1,2,…,m$, then $\{\exp(\lambda_nz)\}$, $\lambda_n\in\Lambda$, is a basis in the space $E^p(D)$, $1<p<\infty$.
Bibliography: 16 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1979, 13:2, 387–404

Bibliographic databases:

UDC: 517.5
MSC: Primary 30H05, 46E15; Secondary 46J15
Received: 02.03.1978

Citation: A. M. Sedletskii, “Bases of exponential functions in the spaces $E^p$ on convex polygons”, Izv. Akad. Nauk SSSR Ser. Mat., 42:5 (1978), 1101–1119; Math. USSR-Izv., 13:2 (1979), 387–404

Citation in format AMSBIB
\Bibitem{Sed78}
\by A.~M.~Sedletskii
\paper Bases of exponential functions in the spaces~$E^p$ on convex polygons
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1978
\vol 42
\issue 5
\pages 1101--1119
\mathnet{http://mi.mathnet.ru/izv1928}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=513915}
\zmath{https://zbmath.org/?q=an:0432.30038|0412.30034}
\transl
\jour Math. USSR-Izv.
\yr 1979
\vol 13
\issue 2
\pages 387--404
\crossref{https://doi.org/10.1070/IM1979v013n02ABEH002050}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1979JD23800009}


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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, “Decomposition of an analytic function into a sum of periodic functions”, Math. USSR-Izv., 25:1 (1985), 163–181  mathnet  crossref  mathscinet  zmath
    2. 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
    3. A. M. Sedletskii, “On Zeros of Functions of Mittag-Leffler Type”, Math. Notes, 68:5 (2000), 602–613  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    4. A. Yu. Popov, A. M. Sedletskii, “Distribution of roots of Mittag-Leffler functions”, Journal of Mathematical Sciences, 190:2 (2013), 209–409  mathnet  crossref  mathscinet  zmath
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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