FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

1999, VOLUME 5, NUMBER 3, PAGES 817-841

On inversion of the generalized Borel transform

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 $[A,+$¥ ), 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 $[A,+$¥ ) for $A$ from a dense class of comparison functions of infinite order.

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Location: http://mech.math.msu.su/~fpm/eng/99/993/99313h.htm
Last modified: November 11, 1999