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St. Petersburg Mathematical Journal
St. Petersburg Mathematical Journal
ISSN 1547-7371(online) ISSN 1061-0022(print)

Singular points of the sum of a series of exponential monomials on the boundary of the convergence domain


Author: O. A. Krivosheyeva
Translated by: S. Kislyakov
Original publication: Algebra i Analiz, tom 23 (2011), nomer 2.
Journal: St. Petersburg Math. J. 23 (2012), 321-350
MSC (2010): Primary 30B50
Published electronically: January 24, 2012
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Abstract | References | Similar Articles | Additional Information

Abstract: Singular points for the sum of a series of exponential monomials are studied. The main statement contains results of Hadamard, Fabry, V. Bernstein, Polya, Carlson and Landau as particular cases. Moreover, a special function is constructed that has no singular points on the boundary of the convergence domain of its series. This function generalizes a certain special function in the theory of Dirichlet series to the case of series of exponential monomials. The existence of this special function shows the necessity of a condition in the main theorem; in V. Bernstein's theorem, a similar role is played by the requirement that the condensation index should be equal to zero.


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Additional Information

O. A. Krivosheyeva
Affiliation: Bashkir State University, Zaki Validi st. 32, Ufa 450074, Russia
Email: kriolesya2006@yandex.ru

DOI: http://dx.doi.org/10.1090/S1061-0022-2012-01199-4
PII: S 1061-0022(2012)01199-4
Keywords: Series of exponentials, convex domain, singular point
Received by editor(s): July 17, 2009
Published electronically: January 24, 2012
Article copyright: © Copyright 2012 American Mathematical Society