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Zapiski Nauchnykh Seminarov POMI, 1997, Volume 247, Pages 276–297 (Mi znsl576)  

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

Concerning an analog of the Stolz angle for the unit ball in $\mathbb C^n$

N. A. Shirokov

Saint-Petersburg State Electrotechnical University
Full-text PDF (287 kB) Citations (1)
Abstract: By a $(\rho,c,q)$-wedge in the unit ball $\mathbb B^n\subset\mathbb C^n$ we mean the union of the sets $\mathbb B^n_\rho$ and $E_{c,q}(e_0)$, where $\mathbb B^n_\rho=\{z\in\mathbb C^n:|z|\le\rho\}$, $0<\rho<1$, $|e_0|=1$, $0<q<1$, $\rho>1-\frac{(1-q)^2}{2(1+c^2)}$,
\begin{gather*} E_{c,q}(e_0)=\{z\in\mathbb B^n:|\operatorname{Im}(1-(z,e_0))|\le c\operatorname{Re}(1-(z,e_0)); \\ |z|^2-|(z,e_0)|^2\le q(1-|(z,e_0)|^2)\} \end{gather*}
($(z,\xi)$ is the usual scalar product in $\mathbb C^n$). We denote by $T_a$, $a\in\mathbb B^n$, $a\ne0$, the intersection of $\mathbb B^n$ and the hyperplane $\{z:(z,a)=|a|^2\}$. The paper contains a description of the sets $Z$ of the form $\bigcup\limits_{a\in A} T_a$, where $A$ belongs to a finite union of $(\rho,c,q)$-wedges with $0<q<\frac12$ that may occur as zero-sets or interpolation sets for functions belonging to $H^\infty(\mathbb B^n)$.
Received: 04.11.1996
English version:
Journal of Mathematical Sciences (New York), 2000, Volume 101, Issue 3, Pages 3216–3229
DOI: https://doi.org/10.1007/BF02673746
Bibliographic databases:
UDC: 517.5
Language: Russian
Citation: N. A. Shirokov, “Concerning an analog of the Stolz angle for the unit ball in $\mathbb C^n$”, Investigations on linear operators and function theory. Part 25, Zap. Nauchn. Sem. POMI, 247, POMI, St. Petersburg, 1997, 276–297; J. Math. Sci. (New York), 101:3 (2000), 3216–3229
Citation in format AMSBIB
\Bibitem{Shi97}
\by N.~A.~Shirokov
\paper Concerning an analog of the Stolz angle for the unit ball in~$\mathbb C^n$
\inbook Investigations on linear operators and function theory. Part~25
\serial Zap. Nauchn. Sem. POMI
\yr 1997
\vol 247
\pages 276--297
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl576}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1692663}
\zmath{https://zbmath.org/?q=an:0961.32007}
\transl
\jour J. Math. Sci. (New York)
\yr 2000
\vol 101
\issue 3
\pages 3216--3229
\crossref{https://doi.org/10.1007/BF02673746}
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  • https://www.mathnet.ru/eng/znsl/v247/p276
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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