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Sibirskii Matematicheskii Zhurnal, 2007, Volume 48, Number 2, Pages 458–473 (Mi smj39)  

This article is cited in 6 scientific papers (total in 6 papers)

Nontrivial expansions of zero and representation of analytic functions by series of simple fractions

V. B. Sherstyukov

Moscow Engineering Physics Institute (State University)
Full-text PDF (296 kB) Citations (6)
References:
Abstract: We propose a modification of the previously-known abstract scheme that reduces the problem of expansion of elements of a locally convex space in series over the system of eigenvectors of some linear operator to the question of existence of a nontrivial expansion of zero in this space. We implement this general scheme for the spaces of analytic functions in domains of the extended complex plane and the systems of simple fractions that are the eigenfunctions of the Pommier operator.
Keywords: absolutely representing system, nontrivial expansion of zero, generalized Laplace transform, representation and convolution operator, Pommier operator, Wolff–Denjoy series.
Received: 13.10.2005
English version:
Siberian Mathematical Journal, 2007, Volume 48, Issue 2, Pages 369–381
DOI: https://doi.org/10.1007/s11202-007-0039-8
Bibliographic databases:
UDC: 517.9
Language: Russian
Citation: V. B. Sherstyukov, “Nontrivial expansions of zero and representation of analytic functions by series of simple fractions”, Sibirsk. Mat. Zh., 48:2 (2007), 458–473; Siberian Math. J., 48:2 (2007), 369–381
Citation in format AMSBIB
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\pages 458--473
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Linking options:
  • https://www.mathnet.ru/eng/smj39
  • https://www.mathnet.ru/eng/smj/v48/i2/p458
  • This publication is cited in the following 6 articles:
    1. S. N. Melikhov, “Coefficients of exponential series for analytic functions and the Pommiez operator”, J. Math. Sci. (N. Y.), 257:2 (2021), 206–245  mathnet  crossref  mathscinet
    2. O. A. Ivanova, S. N. Melikhov, “On operators which commute with the Pommiez type operator in weighted spaces of entire functions”, St. Petersburg Math. J., 28:2 (2017), 209–224  mathnet  crossref  mathscinet  isi  elib
    3. O. A. Ivanova, S. N. Melikhov, “On A. F. Leont'ev's interpolating function”, Ufa Math. J., 6:3 (2014), 17–27  mathnet  crossref  mathscinet  isi  elib
    4. V. B. Sherstyukov, “Dual characterization of absolutely representing systems in inductive limits of Banach spaces”, Siberian Math. J., 51:4 (2010), 745–754  mathnet  crossref  mathscinet  isi  elib  elib
    5. A. L. Myl'nikov, “Minimal Involution-Free Nongroup Reduced Twisted Subsets”, Math. Notes, 88:6 (2010), 860–867  mathnet  mathnet  crossref  crossref  isi  scopus
    6. A. L. Myl'nikov, “Minimal non-group twisted subsets containing involutions”, Algebra and Logic, 46:4 (2007), 250–262  mathnet  mathnet  crossref  isi  scopus
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Сибирский математический журнал Siberian Mathematical Journal
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    Full-text PDF :206
    References:48
     
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