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Zapiski Nauchnykh Seminarov POMI, 1996, Volume 226, Pages 69–79
(Mi znsl3722)
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This article is cited in 4 scientific papers (total in 4 papers)
On value regions of a functional system in the class of typically real functions
E. G. Goluzina St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences
Abstract:
Let $T_R$ be the class of functions
$$
f(z)=z+\sum^\infty_{n=2}c_nz^n
$$
that are regular and typically real in the disk $E=\{z\colon|z|<1\}$. For this class, the region of values of the system $\{f(z_0),f(r)\}$ for $z_0\in E$, $r\in(-1,1)$ is studied. The sets
\begin{align*}
D_r=\{w\colon w=f(z_0),\ f\in T_R,\ f(r)=a\}\quad&\text{for}\quad-1\le r\le1,\\
\Delta_r=\{(c_2,c_3)\colon f\in T_R,\ -f(-r)=a\}\quad&\text{for}\quad0<r\le1
\end{align*}
are found, where $(r(1+r)^{-2},r(1-r)^{-2})$ is an arbitrary fixed number. Bibl. 11 titles.
Received: 20.10.1995
Citation:
E. G. Goluzina, “On value regions of a functional system in the class of typically real functions”, Analytical theory of numbers and theory of functions. Part 13, Zap. Nauchn. Sem. POMI, 226, POMI, St. Petersburg, 1996, 69–79; J. Math. Sci. (New York), 89:1 (1998), 958–966
Linking options:
https://www.mathnet.ru/eng/znsl3722 https://www.mathnet.ru/eng/znsl/v226/p69
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Abstract page: | 75 | Full-text PDF : | 28 |
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