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Mat. Sb., 2009, Volume 200, Number 3, Pages 147–160 (Mi msb4034)  

This article is cited in 3 scientific papers (total in 3 papers)

Representation of the reciprocal of an entire function by series of partial fractions and exponential approximation

V. B. Sherstyukov

Moscow Engineering Physics Institute (National Nuclear Research University)

Abstract: Conditions under which the reciprocal $1/L(\lambda)$ of an entire function with simple zeros $\lambda_k$ can be represented as a series of partial fractions $c_k/(\lambda-\lambda_k)$, $k=1,2,…$, are investigated. The possibility of such a representation is characterized, as is conventional, in terms of a particular ‘asymptotically regular’ behaviour of the function $L(\lambda)$. Applications to complete systems of exponentials on a line interval and to representative systems of exponentials in a convex domain are considered.
Bibliography: 18 titles.

Keywords: entire function, series of partial fractions, representative systems of exponentials.

DOI: https://doi.org/10.4213/sm4034

Full text: PDF file (549 kB)
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English version:
Sbornik: Mathematics, 2009, 200:3, 455–469

Bibliographic databases:

UDC: 517.547.2
MSC: Primary 30D20; Secondary 30B99
Received: 12.11.2007 and 31.07.2008

Citation: V. B. Sherstyukov, “Representation of the reciprocal of an entire function by series of partial fractions and exponential approximation”, Mat. Sb., 200:3 (2009), 147–160; Sb. Math., 200:3 (2009), 455–469

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. V. B. Sherstyukov, “Expanding the reciprocal of an entire function with zeros in a strip in a Kreǐn series”, Sb. Math., 202:12 (2011), 1853–1871  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    2. Ufa Math. J., 8:2 (2016), 104–111  mathnet  crossref  isi  elib
    3. V. B. Sherstyukov, “Asimptoticheskie svoistva tselykh funktsii s zadannym zakonom raspredeleniya kornei”, Kompleksnyi analiz. Tselye funktsii i ikh primeneniya, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 161, VINITI RAN, M., 2019, 104–129  mathnet  mathscinet
  • Математический сборник Sbornik: Mathematics (from 1967)
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