This article is cited in 2 papers

On nontrivial solutions of the homogeneous Abel problem

Yu. A. Kaz'min


Abstract: Let $K$ denote the set of all entire functions $F(z)$ of finite exponential type with the following growth characteristic along the imaginary axis:
$$ F(iy)=O(|y|^Ne^{\frac\pi2|y|}),\qquad y\to\infty\quad(N\geqslant0). $$
It is shown in this paper that the general solution of the symmetric Abel interpolation problem
$$ F^{(n)}(\pm n)=0,\qquad n=0,1,2,\dots, $$
in the class $K$ is of the form $F(z)=C\sin(\pi z/2)$, where $C$ is an arbitrary constant.
Bibliography: 10 titles.

UDC: 517.53

MSC: Primary 30E05; Secondary 30D15

Received: 16.10.1978

 English version: Mathematics of the USSR-Sbornik, 1980, 37:2, 227–244

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