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Matematicheskie Zametki, 2023, Volume 114, Issue 4, Pages 563–578
DOI: https://doi.org/10.4213/mzm13794
(Mi mzm13794)
 

Domain of Existence of the Sum of a Series of Exponential Monomials

A. S. Krivosheeva, O. A. Krivosheevab

a Institute of Mathematics with Computing Centre — Subdivision of the Ufa Federal Research Centre of the Russian Academy of Sciences, Ufa
b Ufa University of Science and Technology
References:
Abstract: In the paper, series of exponential monomials are considered. We study the problem of the distribution of singular points of the sum of a series on the boundary of its domain of convergence. We study the conditions under which, for any sequence of coefficients of the series with a chosen domain of convergence, the domain of existence of the sum of this series coincides with the given domain of convergence. We consider sequences of exponents having an angular density (measurable) and the zero condensation index. Various criteria related to the distribution of singular points of the sum of a series of exponential monomials on the boundary of its convergence domain are obtained. In particular, in the class of the indicated sequences, a criterion is obtained that all boundary points of a chosen convex domain are special for any sum of a series with a given domain of convergence. The criteria are formulated using simple geometric characteristics of the sequence of exponents and a convex domain (the angular density and the length of the boundary arc). It is also shown that the condition that the condensation index is equal to zero is essential.
Keywords: series, domain of convergence, exponential monomial, condensation index, singular point, angular density.
Funding agency Grant number
Foundation for the Development of Theoretical Physics and Mathematics BASIS
The work of the second author was financially supported by the competition “Young Mathematics of Russia”.
Received: 06.11.2022
Revised: 12.02.2023
English version:
Mathematical Notes, 2023, Volume 114, Issue 4, Pages 508–521
DOI: https://doi.org/10.1134/S0001434623090213
Bibliographic databases:
Document Type: Article
UDC: 517
MSC: 30B50
Language: Russian
Citation: A. S. Krivosheev, O. A. Krivosheeva, “Domain of Existence of the Sum of a Series of Exponential Monomials”, Mat. Zametki, 114:4 (2023), 563–578; Math. Notes, 114:4 (2023), 508–521
Citation in format AMSBIB
\Bibitem{KriKri23}
\by A.~S.~Krivosheev, O.~A.~Krivosheeva
\paper Domain of Existence of the Sum of a Series of Exponential Monomials
\jour Mat. Zametki
\yr 2023
\vol 114
\issue 4
\pages 563--578
\mathnet{http://mi.mathnet.ru/mzm13794}
\crossref{https://doi.org/10.4213/mzm13794}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4658800}
\transl
\jour Math. Notes
\yr 2023
\vol 114
\issue 4
\pages 508--521
\crossref{https://doi.org/10.1134/S0001434623090213}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85174597105}
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  • https://www.mathnet.ru/eng/mzm13794
  • https://doi.org/10.4213/mzm13794
  • https://www.mathnet.ru/eng/mzm/v114/i4/p563
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