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Mat. Sb., 2011, Volume 202, Number 8, Pages 3–20 (Mi msb7684)  

This article is cited in 1 scientific paper (total in 1 paper)

Extremal properties of sequences of zeros of analytic functions in spaces with mixed norm

A. A. Dolgoborodov, E. A. Sevast'yanov

National Engineering Physics Institute "MEPhI", Moscow

Abstract: Functions whose sequences of absolute values of zeros have certain extremal properties are constructed in Bergmann spaces with powerlike weight and in more general spaces with mixed norm. These properties can be expressed in terms of subsequences with indices satisfying certain necessary and sufficient conditions. In particular, using these functions it is possible to distinguish between the zero sets of the spaces in question in some cases which have not previously been investigated. This reveals the significant role which subsequences of zeros in general play in the solution of this type of problems.
Bibliography: 8 titles.

Keywords: Bergmann spaces, zeros of analytic functions.

DOI: https://doi.org/10.4213/sm7684

Full text: PDF file (546 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2011, 202:8, 1085–1103

Bibliographic databases:

Document Type: Article
UDC: 517.53
MSC: 30C15
Received: 28.01.2010 and 26.05.2011

Citation: A. A. Dolgoborodov, E. A. Sevast'yanov, “Extremal properties of sequences of zeros of analytic functions in spaces with mixed norm”, Mat. Sb., 202:8 (2011), 3–20; Sb. Math., 202:8 (2011), 1085–1103

Citation in format AMSBIB
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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, “On zeros of functions rapidly growing in generalized Bergman spaces”, Russian Math. (Iz. VUZ), 61:11 (2017), 40–52  mathnet  crossref  isi
  • Математический сборник Sbornik: Mathematics (from 1967)
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