Geodesic
Convergence of series of exponential monomials
Ufa mathematical journal, Tome 14 (2022) no. 4, pp. 56-68

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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, Abel theorem, Cauchy-Hadamard theorem.
Mots-clés : convex domain 
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     author = {A. S. Krivosheev and O. A. Krivosheeva},
     title = {Convergence of series of exponential monomials},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/UFA_2022_14_4_a4/}
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A. S. Krivosheev; O. A. Krivosheeva. Convergence of series of exponential monomials. Ufa mathematical journal, Tome 14 (2022) no. 4, pp. 56-68. http://geodesic.mathdoc.fr/item/UFA_2022_14_4_a4/