FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA
(FUNDAMENTAL AND APPLIED MATHEMATICS)
1999, VOLUME 5, NUMBER 3, PAGES 817-841
A. Yu. Popov
Abstract
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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.
All articles are published in Russian.
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Last modified: November 11, 1999