RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Forthcoming papers Archive Impact factor Subscription Guidelines for authors License agreement Submit a manuscript Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Mat. Zametki: Year: Volume: Issue: Page: Find

 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

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}