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Izv. RAN. Ser. Mat., 2000, Volume 64, Issue 5, Pages 69–132 (Mi izv305)  

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.

DOI: https://doi.org/10.4213/im305

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English version:
Izvestiya: Mathematics, 2000, 64:5, 939–1001

Bibliographic databases:

MSC: 45E10
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

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. S. Krivosheev, S. N. Gantsev, “Solvability of systems of nonhomogeneous convolution equations in convex domains in $\mathbb C^1$”, St. Petersburg Math. J., 15:6 (2004), 847–865  mathnet  crossref  mathscinet  zmath
    2. V. V. Napalkov, S. G. Merzlyakov, “Neodnorodnye sistemy uravnenii svertki v kompleksnoi oblasti”, Vladikavk. matem. zhurn., 7:3 (2005), 50–55  mathnet  mathscinet  elib
    3. G. G. Braichev, V. B. Sherstyukov, “Tochnye otsenki asimptoticheskikh kharakteristik rosta tselykh funktsii s nulyami na zadannykh mnozhestvakh”, Fundament. i prikl. matem., 22:1 (2018), 51–97  mathnet
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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