Singular points of the sum of a series of exponential monomials on the boundary of the convergence domain
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O. A. Krivosheyeva
Translated by: S. Kislyakov - St. Petersburg Math. J. 23 (2012), 321-350
- DOI: https://doi.org/10.1090/S1061-0022-2012-01199-4
- Published electronically: January 24, 2012
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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.References
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Bibliographic Information
- O. A. Krivosheyeva
- Affiliation: Bashkir State University, Zaki Validi st. 32, Ufa 450074, Russia
- Email: kriolesya2006@yandex.ru
- Received by editor(s): July 17, 2009
- Published electronically: January 24, 2012
- © Copyright 2012 American Mathematical Society
- Journal: St. Petersburg Math. J. 23 (2012), 321-350
- MSC (2010): Primary 30B50
- DOI: https://doi.org/10.1090/S1061-0022-2012-01199-4
- MathSciNet review: 2841675