A. Yu. Popov, On inversion of the generalized Borel transform

Title: On inversion of the generalized Borel transform
Authors: A. Yu. Popov
Journal title: Fundam. Prikl. Mat.
Year: 1999
Issue: 3
Volume: 5
Pages: 817-841

A. Yu. Popov, “On inversion of the generalized Borel transform”, Fundam. Prikl. Mat., 5:3 (1999), 817–841


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 <span id=[A,+?)" />, where <span id=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 <span id=[A,+?)" /> for A from a dense class of comparison functions of infinite order.