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Sbornik: Mathematics, 2009, Volume 200, Issue 3, Pages 455–469
DOI: https://doi.org/10.1070/SM2009v200n03ABEH004004
(Mi sm4034)
 

This article is cited in 4 scientific papers (total in 4 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)
References:
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 $c_k/(\lambda-\lambda_k)$, $k=1,2,\dots$, 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.
Received: 12.11.2007 and 31.07.2008
Russian version:
Matematicheskii Sbornik, 2009, Volume 200, Number 3, Pages 147–160
DOI: https://doi.org/10.4213/sm4034
Bibliographic databases:
UDC: 517.547.2
MSC: Primary 30D20; Secondary 30B99
Language: English
Original paper language: Russian
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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  • https://www.mathnet.ru/eng/sm4034
  • https://doi.org/10.1070/SM2009v200n03ABEH004004
  • https://www.mathnet.ru/eng/sm/v200/i3/p147
  • 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
    Математический сборник Sbornik: Mathematics
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    Abstract page:888
    Russian version PDF:231
    English version PDF:12
    References:92
    First page:16
     
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