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Convergence of series of exponential monomials
A. S. Krivosheeva, O. A. Krivosheevab a Institute of Mathematics,
Ufa Federal Research Center, RAS,
Chernyshevsky str. 112,
450008, Ufa, Russia
b Bashkir State University,
Zaki Validi str. 32,
450076, Ufa, Russia
Abstract:
In the paper we study the convergence of series of exponential monomials, special cases of which are the series of exponentials, Dirichlet series and power series. We provide a description of the space of coefficients of series of exponential monomials converging in a given convex domain in the complex plane is described. Under a single natural restriction on the degrees of monomials, we provide a complete analogue of the Abel theorem for such series, which, in particular, implies results on the continued convergence of series of exponential monomials. We also obtain a complete analogue of the Cauchy-Hadamard theorem, in which we give a formula allowing to recover the convergence domain of these series by their coefficients. The obtained results
include, as special cases, all previously known results related
with the Abel and Cauchy-Hadamard theorems for exponential series, Dirichlet series and power series.
Keywords:
exponential monomial, convex domain, Abel theorem, Cauchy-Hadamard theorem.
Received: 20.09.2022
Citation:
A. S. Krivosheev, O. A. Krivosheeva, “Convergence of series of exponential monomials”, Ufimsk. Mat. Zh., 14:4 (2022), 60–72; Ufa Math. J., 14:4 (2022), 56–68
Linking options:
https://www.mathnet.ru/eng/ufa637https://doi.org/10.13108/2022-14-4-56 https://www.mathnet.ru/eng/ufa/v14/i4/p60
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Abstract page: | 61 | Russian version PDF: | 20 | English version PDF: | 26 | References: | 17 |
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