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Fundam. Prikl. Mat., 1999, Volume 5, Issue 3, Pages 817–841 (Mi fpm414)  

This article is cited in 2 scientific papers (total in 2 papers)

On inversion of the generalized Borel transform

A. Yu. Popov

M. V. Lomonosov Moscow State University

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.

Full text: PDF file (994 kB)

Bibliographic databases:
UDC: 517.547.2
Received: 01.12.1996

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://www.ams.org/mathscinet-getitem?mr=1806858}
\zmath{https://zbmath.org/?q=an:0961.30019}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. Yu. Popov, “Bounds for convergence and uniqueness in Abel–Goncharov interpolation problems”, Sb. Math., 193:2 (2002), 247–277  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. A. Yu. Popov, “On the completeness of sparse subsequences of systems of functions of the form $f^{(n)}(\lambda_nz)$”, Izv. Math., 68:5 (2004), 1025–1049  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
  • Фундаментальная и прикладная математика
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