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Ufimsk. Mat. Zh., 2011, Volume 3, Issue 3, Pages 152–163 (Mi ufa110)  

Stability of sequences of zeros for classes of holomorphic functions of moderate growth in the unit disk

F. B. Khabibullin

Bashkir State University, Ufa, Russia

Abstract: Let $\Lambda=(\lambda_k)$ and $\Gamma=(\gamma_k)$ be two sequences of points in the unit disk $\mathbb D:=ż\in\mathbb C\colon|z|<1\}$ of the complex plane $\mathbb C$, and $H$ be a weight space of holomorphic functions on $\mathbb D$. Suppose that $\Lambda$ is the zero subsequence of some nonzero function from $H$. We give conditions of closeness of the sequence $\Gamma $ to the sequence $\Lambda$, under which the sequence $\Gamma$ is the zero sequence for some holomorphic function from space $\hat H\supset H$. The space $\hat H$ can be a little larger than $H$.

Keywords: holomorphic function, unit disk, weight space, zero sequence, zero subsequence, shift of zeros, stability of zero sequence.

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Bibliographic databases:
UDC: 517.547
Received: 15.07.2011

Citation: F. B. Khabibullin, “Stability of sequences of zeros for classes of holomorphic functions of moderate growth in the unit disk”, Ufimsk. Mat. Zh., 3:3 (2011), 152–163

Citation in format AMSBIB
\Bibitem{Kha11}
\by F.~B.~Khabibullin
\paper Stability of sequences of zeros for classes of holomorphic functions of moderate growth in the unit disk
\jour Ufimsk. Mat. Zh.
\yr 2011
\vol 3
\issue 3
\pages 152--163
\mathnet{http://mi.mathnet.ru/ufa110}
\zmath{https://zbmath.org/?q=an:1249.30012}


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