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

Автор(и)

  • S. L. Gefter B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine, 47 Lenin Ave., Kharkov, 61103, Ukraine
  • V .N. Mokrenyuk LLC "OMEGA-Avtopostavka", st. Promyshlennaya, 1, village Vasishchevo, Kharkov district, Kharkov region, 62495, Ukraine

Ключові слова:

divergent series, differential equations, Banach space

Анотація

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 $\displaystyle\sum^{\infty}_{n=0}c_nA^nz^n$, $c_n\in \mathbb{C}$ are considered.

Mathematics Subject Classification: 34A20, 34A25, 34G10.

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Як цитувати

(1)
Gefter, S. L.; Mokrenyuk, V. .N. The power series $\displaystyle\sum^{\infty}_{n=0}n!z^n$ and holomorphic solutions of some differential equations in a Banach space. Журн. мат. фіз. анал. геом. 2005, 1, 53-70.

Номер

Том 1 № 1 (2005)

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