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Mat. Zametki, 2013, Volume 94, Issue 2, Pages 279–294 (Mi mz8964)  

This article is cited in 2 scientific papers (total in 3 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 $ż_{n_k}(f)\}$ 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.

DOI: https://doi.org/10.4213/mzm8964

Full text: PDF file (542 kB)
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English version:
Mathematical Notes, 2013, 94:2, 266–280

Bibliographic databases:

UDC: 517.53
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

Citation in format AMSBIB
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  • http://mi.mathnet.ru/eng/mz/v94/i2/p279

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. E. A. Sevast'yanov, A. A. Dolgoborodov, “Letter to the Editor”, Math. Notes, 94:2 (2013), 301–304  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    2. E. A. Sevast'yanov, “On zeros of functions rapidly growing in generalized Bergman spaces”, Russian Math. (Iz. VUZ), 61:11 (2017), 40–52  mathnet  crossref  isi
    3. R. Lyons, A. Zhai, “Zero sets for spaces of analytic functions”, Ann. Inst. Fourier, 68:6 (2018), 2311–2328  crossref  zmath  isi
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