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Zap. Nauchn. Sem. POMI, 2005, Volume 327, Pages 226–234 (Mi znsl332)  

This article is cited in 1 scientific paper (total in 1 paper)

On the cyclic elements of the shift operator in a weighted anisotropic space of holomorphic function in the polydisc

F. A. Shamoyan

I. G. Petrovsky Bryansk State University

Abstract: Let $\varphi(r)=(\varphi_1(r_1),…,\varphi_n(r_n))$ be a vector-valued function on $\mathbf R^n_+$. A necessary and sufficiently condition is obtained for every $f\in H^\infty(\mathbf D^n)$, $f(z)\ne 0$, $z\in \mathbf D^n$ to be cyclic in the corresponding $L^p(\varphi)$ weighted space, where $\mathbf D^n$ is unit polydisc in $\mathbf C^n$.

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English version:
Journal of Mathematical Sciences (New York), 2006, 139:2, 6491–6495

Bibliographic databases:

UDC: 517.55
Received: 22.09.2005

Citation: F. A. Shamoyan, “On the cyclic elements of the shift operator in a weighted anisotropic space of holomorphic function in the polydisc”, Investigations on linear operators and function theory. Part 33, Zap. Nauchn. Sem. POMI, 327, POMI, St. Petersburg, 2005, 226–234; J. Math. Sci. (N. Y.), 139:2 (2006), 6491–6495

Citation in format AMSBIB
\Bibitem{Sha05}
\by F.~A.~Shamoyan
\paper On the cyclic elements of the shift operator in a~weighted anisotropic space of holomorphic function in the polydisc
\inbook Investigations on linear operators and function theory. Part~33
\serial Zap. Nauchn. Sem. POMI
\yr 2005
\vol 327
\pages 226--234
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl332}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2184757}
\zmath{https://zbmath.org/?q=an:1103.47007}
\elib{http://elibrary.ru/item.asp?id=9127032}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2006
\vol 139
\issue 2
\pages 6491--6495
\crossref{https://doi.org/10.1007/s10958-006-0365-6}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33750198209}


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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. F. A. Shamoyan, “A weak invertibility criterion in the weighted $L^p$-spaces of holomorphic functions in the ball”, Siberian Math. J., 50:6 (2009), 1115–1132  mathnet  crossref  mathscinet  isi  elib  elib
  • Записки научных семинаров ПОМИ
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