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Fundamentalnaya i Prikladnaya Matematika, 1999, Volume 5, Issue 3, Pages 817–841 (Mi fpm414)  

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

On inversion of the generalized Borel transform

A. Yu. Popov

M. V. Lomonosov Moscow State University
Full-text PDF (994 kB) Citations (3)
Abstract: The generalized Borel transform has a lot of applications in the theory of entire functions. It is defined on the space of functions analytic in a neighborhood of infinity and vanishing at infinity and takes values on a class $[A,+\infty)$, where $A$ is a comparison function. In this paper we obtain an integral representation of inverse generalized Borel transform for a dense class of comparison functions. This allows us to prove an analog of Polya theorem on analytic continuation of inverse Borel transform of functions of $[A,+\infty)$ for $A$ from a dense class of comparison functions of infinite order.
Received: 01.12.1996
Bibliographic databases:
UDC: 517.547.2
Language: Russian
Citation: A. Yu. Popov, “On inversion of the generalized Borel transform”, Fundam. Prikl. Mat., 5:3 (1999), 817–841
Citation in format AMSBIB
\Bibitem{Pop99}
\by A.~Yu.~Popov
\paper On inversion of the~generalized Borel transform
\jour Fundam. Prikl. Mat.
\yr 1999
\vol 5
\issue 3
\pages 817--841
\mathnet{http://mi.mathnet.ru/fpm414}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1806858}
\zmath{https://zbmath.org/?q=an:0961.30019}
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  • https://www.mathnet.ru/eng/fpm414
  • https://www.mathnet.ru/eng/fpm/v5/i3/p817
  • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Фундаментальная и прикладная математика
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