Article
Ufa Mathematical Journal
Volume 3, Number 3, pp. 146-157
Stability of sequences of zero for classes of holomorphic functions of moderate growth in the unit disk
Khabibullin F.B.
Download PDF
Article on MathNetAbstact
Let $\Lambda = (\lambda_k ) $ and $ \Gamma = (\gamma_k ) $ are two point sequences in the unit disk $ \D: = \{z\in \bC \colon |z | <1 \} $ of the complex plane $ \bC $, and $H $ be a weight space of holomorphic functions on $\D$. 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 more than $H $.