Geodesic
The convergence domain for series of exponential monomials
Ufa mathematical journal, Tome 3 (2011) no. 2, pp. 42-55 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Questions of convergence for exponential series of monomials are studied in this paper. Exponential series, Dirichlet's series and power series are particular cases of these series. The space of coefficients of exponential series of monomials converging in the given convex domain in a complex plane is described. The full analogue of Abel's theorem for these series is formulated with a natural restriction. In particular, results on continuation of convergence of exponential series follow from this analogue. A full analogue of Cauchy–Hadamard's theorem is obtained as well. It provides a formula for finding the convergence domain of these series by their coefficients. The obtained results include all earlier known results connected with Abel and Cauchy–Hadamard's theorems for exponential series, Dirichlet's series and power series as particular cases.
Keywords: exponential series, analytic function.
Mots-clés : convex domain 
@article{UFA_2011_3_2_a5,
     author = {O. A. Krivosheyeva},
     title = {The convergence domain for series of exponential monomials},
     journal = {Ufa mathematical journal},
     pages = {42--55},
     year = {2011},
     volume = {3},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/UFA_2011_3_2_a5/}
}
TY  - JOUR
AU  - O. A. Krivosheyeva
TI  - The convergence domain for series of exponential monomials
JO  - Ufa mathematical journal
PY  - 2011
SP  - 42
EP  - 55
VL  - 3
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/UFA_2011_3_2_a5/
LA  - en
ID  - UFA_2011_3_2_a5
ER  - 
%0 Journal Article
%A O. A. Krivosheyeva
%T The convergence domain for series of exponential monomials
%J Ufa mathematical journal
%D 2011
%P 42-55
%V 3
%N 2
%U http://geodesic.mathdoc.fr/item/UFA_2011_3_2_a5/
%G en
%F UFA_2011_3_2_a5
O. A. Krivosheyeva. The convergence domain for series of exponential monomials. Ufa mathematical journal, Tome 3 (2011) no. 2, pp. 42-55. http://geodesic.mathdoc.fr/item/UFA_2011_3_2_a5/

[1] Leontev A. F., Ryady eksponent, Nauka, M., 1976 | MR

[2] Leontev A. F., Tselye funktsii. Ryady eksponent, Nauka, M., 1983 | MR

[3] E. Hille, “Note on Dirichlet's series with complex exponents”, Ann. of Math., 25 (1924), 261–278 | DOI | MR | Zbl

[4] Lunts G. L., “O nekotorykh obobscheniyakh ryadov Dirikhle”, Matem. sb., 10(52):1–2 (1942), 33–50 | MR | Zbl

[5] Lunts G. L., “Ob odnom klasse obobschennykh ryadov Dirikhle”, UMN, 12:3(75) (1957), 173–179 | MR | Zbl

[6] Bratischev A. V., Bazisy Kete, tselye funktsii i ikh prilozheniya, Diss. na soiskanie uch. st. dokt. fiz.-mat. nauk, Rostov-na-Donu, 1995

[7] Leikhtveis K., Vypuklye mnozhestva, Nauka, M., 1985 | MR