St. Petersburg Mathematical Journal

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ISSN 1547-7371(e) ISSN 1061-0022(p)

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
Posted: 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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