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Mat. Sb., 2011, Volume 202, Number 12, Pages 137–156 (Mi msb7771)  

This article is cited in 8 scientific papers (total in 8 papers)

Expanding the reciprocal of an entire function with zeros in a strip in a Kreǐn series

V. B. Sherstyukov

Moscow Engineering Physics Institute (National Nuclear Research University)

Abstract: If $L(\lambda)$ is an entire function with only simple zeros, all of which lie in some strip, the problem of representing $L^{-1}(\lambda)$ by a partial fraction series is solved.
Bibliography: 26 titles.

Keywords: entire function, partial fraction series.

DOI: https://doi.org/10.4213/sm7771

Full text: PDF file (589 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2011, 202:12, 1853–1871

Bibliographic databases:

UDC: 517.547.2
MSC: 30B50, 30D10
Received: 06.07.2010 and 01.11.2010

Citation: V. B. Sherstyukov, “Expanding the reciprocal of an entire function with zeros in a strip in a Kreǐn series”, Mat. Sb., 202:12 (2011), 137–156; Sb. Math., 202:12 (2011), 1853–1871

Citation in format AMSBIB
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  • https://doi.org/10.4213/sm7771
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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. V. Sumin, V. B. Sherstyukov, “Application of Kreins series to calculation of sums containing zeros of the Bessel functions”, Comput. Math. Math. Phys., 55:4 (2015), 572–579  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    2. Ufa Math. J., 8:2 (2016), 104–111  mathnet  crossref  isi  elib
    3. Sherstyukov V.B., Sumin E.V., “Reciprocal Expansion of Modified Bessel Function in Simple Fractions and Obtaining General Summation Relationships Containing Its Zeros”, Vi International Conference Problems of Mathematical Physics and Mathematical Modelling, Journal of Physics Conference Series, 937, IOP Publishing Ltd, 2017, UNSP 012047  crossref  isi  scopus
    4. St. Petersburg Math. J., 30:5 (2019), 761–802  mathnet  crossref  mathscinet  isi  elib
    5. Boito P., Eidelman Y., Gemignani L., “Efficient Solution of Parameter-Dependent Quasiseparable Systems and Computation of Meromorphic Matrix Functions”, Numer. Linear Algebr. Appl., 25:6, SI (2018), e2141  crossref  mathscinet  zmath  isi  scopus
    6. 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
    7. Abakumov E., Baranov A., Belov Yu., “Krein-Type Theorems and Ordered Structure For Cauchy-de Branges Spaces”, J. Funct. Anal., 277:1 (2019), 200–226  crossref  mathscinet  zmath  isi
    8. A. R. Mirotin, A. A. Atvinovskii, “O multiplikativnom obraschenii ryadov Volfa - Danzhua”, Tr. IMM UrO RAN, 25, no. 4, 2019, 147–154  mathnet  crossref  elib
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