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Izvestiya: Mathematics, 2000, Volume 64, Issue 5, Pages 939–1001
DOI: https://doi.org/10.1070/im2000v064n05ABEH000305
(Mi im305)
 

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
References:
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
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2000, Volume 64, Issue 5, Pages 69–132
DOI: https://doi.org/10.4213/im305
Bibliographic databases:
MSC: 45E10
Language: English
Original paper language: Russian
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
Citation in format AMSBIB
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\pages 69--132
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  • https://www.mathnet.ru/eng/im305
  • https://doi.org/10.1070/im2000v064n05ABEH000305
  • https://www.mathnet.ru/eng/im/v64/i5/p69
  • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
    Statistics & downloads:
    Abstract page:508
    Russian version PDF:221
    English version PDF:31
    References:116
    First page:2
     
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