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Fundamentalnaya i Prikladnaya Matematika, 1999, Volume 5, Issue 3, Pages 817–841
(Mi fpm414)
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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
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
Citation:
A. Yu. Popov, “On inversion of the generalized Borel transform”, Fundam. Prikl. Mat., 5:3 (1999), 817–841
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https://www.mathnet.ru/eng/fpm414 https://www.mathnet.ru/eng/fpm/v5/i3/p817
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Abstract page: | 384 | Full-text PDF : | 193 | First page: | 1 |
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