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Эта публикация цитируется в 2 научных статьях (всего в 2 статьях)
Singular points for the sum of a series of exponential monomials
O. A. Krivosheevaa, A. S. Krivosheevb a Bashkir State University,
32 Z. Validi, Ufa 450076, Russia
b Institute of Mathematics
with Computing Centre — Subdivision of the Ufa Federal Research Centre
of the Russian Academy of Science,
112 Chernyshevsky str., Ufa 450008, Russia
Аннотация:
A problem of distribution of singular points for sums of series of exponential monomials on the boundary of its convergence domain is studied.
The influence of a multiple sequence $\Lambda=\{\lambda_k, n_k \}_{k=1}^\infty$ of the series in the presence of singular points on the arc of the boundary,
the ends of which are located at a certain distance $R$ from each other, is investigated.
In this regard, the condensation indices of the sequence and the relative multiplicity of its points are considered.
It is proved that the finiteness of the condensation index and the zero relative multiplicity are necessary for the existence of singular points of the series sum on the $R$-arc.
It is also proved that for one of the sequence classes $\Lambda$, these conditions give a criterion.
Special cases of this result are the well-known results for the singular points of the sums of the Taylor and Dirichlet series,
obtained by J. Hadamard, E. Fabry, G. Pólya, W.H.J. Fuchs, P. Malliavin, V. Bernstein and A. F. Leont'ev, etc.
Ключевые слова:
invariant subspace, series of exponential monomials, singular point, convex domain.
Поступила в редакцию: 11.05.2018 Исправленный вариант: 29.08.2018 Принята в печать: 31.08.2018
Образец цитирования:
O. A. Krivosheeva, A. S. Krivosheev, “Singular points for the sum of a series of exponential monomials”, Пробл. анал. Issues Anal., 7(25), спецвыпуск (2018), 72–87
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/pa233 https://www.mathnet.ru/rus/pa/v25/i3/p72
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