Zhurnal Matematicheskoi Fiziki, Analiza, Geometrii [Journal of Mathematical Physics, Analysis, Geometry]
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Zhurnal Matematicheskoi Fiziki, Analiza, Geometrii [Journal of Mathematical Physics, Analysis, Geometry], 2005, Volume 1, Number 1, Pages 53–70 (Mi jmag3)  
This article is cited in 2 scientific papers (total in 2 papers)

The power series $\sum_{n=0}^\infty n!\,z^n$ and holomorphic solutions of some differential equations in a Banach space

S. L. Geftera, V. N. Mokrenyuk

a B. Verkin Institute for Low Temperature Physics and Engineering National Academy of Sciences of Ukraine, 47 Lenin Ave., Kharkov, 61103, Ukraine
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Abstract: Let $A$ be a bounded operator on a Banach space. A question about the existence of holomorphic solutions of the equation $z^2Aw'+g(z)=w$ is studied. Moreover, general properties of power series of the form $\sum_{n=0}^\infty c_nA^nz^n$, $c_n\in\mathbb C$ are considered.
Key words and phrases: divergent series, differential equations, Banach space.
Received: 29.06.2004
Bibliographic databases:
Document Type: Article
MSC: 34A20, 34A25, 34G10
Language: Russian
Citation: S. L. Gefter, V. N. Mokrenyuk, “The power series $\sum_{n=0}^\infty n!\,z^n$ and holomorphic solutions of some differential equations in a Banach space”, Zh. Mat. Fiz. Anal. Geom., 1:1 (2005), 53–70
Citation in format AMSBIB
\Bibitem{GefMok05}
\by S.~L.~Gefter, V.~N.~Mokrenyuk
\paper The power series $\sum_{n=0}^\infty n!\,z^n$ and holomorphic solutions of some differential equations in a Banach space
\jour Zh. Mat. Fiz. Anal. Geom.
\yr 2005
\vol 1
\issue 1
\pages 53--70
\mathnet{http://mi.mathnet.ru/jmag3}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2170084}
\zmath{https://zbmath.org/?q=an:1086.34049}
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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