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Izvestiya: Mathematics, 1997, Volume 61, Issue 4, Pages 795–812
DOI: https://doi.org/10.1070/im1997v061n04ABEH000138
(Mi im138)
 

This article is cited in 1 scientific paper (total in 1 paper)

Certain classes of power series that cannot be analytically continued across their circle of convergence

A. I. Pavlov

Steklov Mathematical Institute, Russian Academy of Sciences
References:
Abstract: We define, in number-theoretical terms, the class $\{M\}$ of sets of natural numbers having the properties:
1) the asymptotic density $\gamma$ of a set $M$ satisfies the inequality $0<\gamma<1$;
2) if $G(z)$ is an entire function with non-negative Taylor coefficients and not growing too fast at infinity, then the power series $\sum_{m\in M}G(m)z^m$, having radius of convergence 1, cannot be analytically continued into the domain $|z|>1$ across any arc on the circle $|z|=1$.
Received: 02.12.1995
Bibliographic databases:
MSC: 30B40
Language: English
Original paper language: Russian
Citation: A. I. Pavlov, “Certain classes of power series that cannot be analytically continued across their circle of convergence”, Izv. Math., 61:4 (1997), 795–812
Citation in format AMSBIB
\Bibitem{Pav97}
\by A.~I.~Pavlov
\paper Certain classes of power series that cannot be analytically continued across their circle of convergence
\jour Izv. Math.
\yr 1997
\vol 61
\issue 4
\pages 795--812
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\crossref{https://doi.org/10.1070/im1997v061n04ABEH000138}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33747401965}
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  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
     
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