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This article is cited in 3 scientific papers (total in 3 papers)
Regular growth of systems of functions and systems of non-homogeneous convolution equations in convex domains of the complex plane
A. S. Krivosheev Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences
Abstract:
In this paper we introduce the notion of regular growth for a system of entire functions of finite order and type. This is a direct and natural generalization of the classical completely regular growth of an entire function. We obtain sufficient and necessary conditions for the solubility of a system of non-homogeneous convolution equations in convex domains of the complex plane. These conditions depend on whether the system of Laplace transforms of the analytic functionals that generate the convolution equations has regular growth. In the case of smooth convex domains, these solubility conditions form a criterion.
Received: 13.04.1999
Citation:
A. S. Krivosheev, “Regular growth of systems of functions and systems of non-homogeneous convolution equations in convex domains of the complex plane”, Izv. RAN. Ser. Mat., 64:5 (2000), 69–132; Izv. Math., 64:5 (2000), 939–1001
Linking options:
https://www.mathnet.ru/eng/im305https://doi.org/10.1070/im2000v064n05ABEH000305 https://www.mathnet.ru/eng/im/v64/i5/p69
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Abstract page: | 508 | Russian version PDF: | 221 | English version PDF: | 31 | References: | 116 | First page: | 2 |
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