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Matematicheskie Zametki, 2013, Volume 94, Issue 2, Pages 279–294
DOI: https://doi.org/10.4213/mzm8964
(Mi mzm8964)
 

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
Full-text PDF (542 kB) Citations (4)
References:
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
English version:
Mathematical Notes, 2013, Volume 94, Issue 2, Pages 266–280
DOI: https://doi.org/10.1134/S0001434613070262
Bibliographic databases:
Document Type: Article
UDC: 517.53
Language: Russian
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
Citation in format AMSBIB
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  • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математические заметки Mathematical Notes
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