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Izv. Akad. Nauk SSSR Ser. Mat., 1988, Volume 52, Issue 5, Pages 1051–1069 (Mi izv1217)  

Projection from the spaces $E^p$ on a convex polygon onto subspaces of periodic functions

A. M. Sedletskii


Abstract: Notation: $D$ is a convex polygon with vertices $a_1,…,a_m$, $P_k$ is the half-plane bounded by the extension of the side $a_k$, $a_{k+1}$ and containing $D$, $E^p$ is the Hardy–Smirnov space on $D$, and $Q_s$ is the subspace of $E^p$ consisting of the analytic functions on $P_k$ that are periodic with period $a_{k+1}-a_k$ and that vanish at $\infty$. For suitable $s$ the subspaces $Q_s$ and $H_1^p,…,H_m^p$ generate $E^p$. Is $E^p$ ($1<p<\infty$) decomposable into their direct sum? If $m$ is odd, then the answer is positive for $p\ne2$ and negative for $p=2$.
Bibliography: 15 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1989, 33:2, 373–390

Bibliographic databases:

UDC: 517.5
MSC: Primary 30C99, 30H05; Secondary 30D55, 30D15
Received: 02.10.1986

Citation: A. M. Sedletskii, “Projection from the spaces $E^p$ on a convex polygon onto subspaces of periodic functions”, Izv. Akad. Nauk SSSR Ser. Mat., 52:5 (1988), 1051–1069; Math. USSR-Izv., 33:2 (1989), 373–390

Citation in format AMSBIB
\Bibitem{Sed88}
\by A.~M.~Sedletskii
\paper Projection from the spaces $E^p$ on a~convex polygon onto subspaces of periodic functions
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1988
\vol 52
\issue 5
\pages 1051--1069
\mathnet{http://mi.mathnet.ru/izv1217}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=972095}
\zmath{https://zbmath.org/?q=an:0722.30021}
\transl
\jour Math. USSR-Izv.
\yr 1989
\vol 33
\issue 2
\pages 373--390
\crossref{https://doi.org/10.1070/IM1989v033n02ABEH000837}


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  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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