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Mat. Zametki, 1972, Volume 12, Issue 6, Pages 681–692 (Mi mz9933)  

The domain of regularity of the limit function of a sequence of analytic functions

V. V. Napalkov

Physics and Mathematics Section of the Bashkir Division of the Academy of Sciences of the USSR

Abstract: Let $f(z)$ be an entire function $\lambda_n$ ($n=0,1,2,…$) complex numbers, such that the system $\{f(\lambda_nz)\}_{n=0}^\infty$ is not complete in the circle $|z|<R$ and let the sequence $Q_n(z)$ have the form $\sum_{k=0}^{p_n}a_{nk}f(\lambda_k\cdot z)$. We study the properties of the limit function of the sequence $Q_n(z)$ in the case when
$$ f(z)=1+\sum_{n=1}^\infty\frac{z^n}{P(1)P(2)…P(n)}, $$
where $P(z)$ is a polynomial having at least one negative integral root.

Full text: PDF file (1120 kB)

English version:
Mathematical Notes, 1972, 12:6, 849–855

Bibliographic databases:

UDC: 517.5
Received: 21.12.1971

Citation: V. V. Napalkov, “The domain of regularity of the limit function of a sequence of analytic functions”, Mat. Zametki, 12:6 (1972), 681–692; Math. Notes, 12:6 (1972), 849–855

Citation in format AMSBIB
\Bibitem{Nap72}
\by V.~V.~Napalkov
\paper The domain of regularity of the limit function of a sequence of analytic functions
\jour Mat. Zametki
\yr 1972
\vol 12
\issue 6
\pages 681--692
\mathnet{http://mi.mathnet.ru/mz9933}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=316689}
\zmath{https://zbmath.org/?q=an:0251.30008}
\transl
\jour Math. Notes
\yr 1972
\vol 12
\issue 6
\pages 849--855
\crossref{https://doi.org/10.1007/BF01156043}


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