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This article is cited in 3 scientific papers (total in 4 papers)
Zeros of Functions in Weighted Spaces with Mixed Norm
E. A. Sevast'yanov, A. A. Dolgoborodov National Engineering Physics Institute "MEPhI", Moscow
Abstract:
In the spaces of analytic functions $f$ in the unit disk with mixed norm and measure satisfying the $\Delta_2$-condition, sharp necessary conditions on subsequences of zeros $\{z_{n_k}(f)\}$ of the function $f$ are obtained in terms of subsequences of numbers $\{n_k\}$. These conditions can be used to define, in the spaces with mixed norm, subsets of functions with certain extremal properties; these subsets provide answers to a number of questions about the zero sets of the spaces under consideration and, in particular, about weighted Bergman spaces.
Keywords:
weighted space with mixed norm, weighted Bergman space, distribution of moduli of zeros, zero set of a function, Hardy space.
Received: 18.10.2010 Revised: 02.09.2012
Citation:
E. A. Sevast'yanov, A. A. Dolgoborodov, “Zeros of Functions in Weighted Spaces with Mixed Norm”, Mat. Zametki, 94:2 (2013), 279–294; Math. Notes, 94:2 (2013), 266–280
Linking options:
https://www.mathnet.ru/eng/mzm8964https://doi.org/10.4213/mzm8964 https://www.mathnet.ru/eng/mzm/v94/i2/p279
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Abstract page: | 360 | Full-text PDF : | 167 | References: | 57 | First page: | 44 |
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