Bernstein-Type Theorems and Uniqueness Theorems |
| |
Authors: | V Logvinenko N Nazarova |
| |
Institution: | (1) Pasadena City College, Pasadena, USA;(2) Kharkov Polytechnic University, Kharkov |
| |
Abstract: | Let
be an entire function of finite type with respect to finite order
and let
be a subset of an open cone in a certain n-dimensional subspace
(the smaller
, the sparser
). We assume that this cone contains a ray
. It is shown that the radial indicator
of
at any point
may be evaluated in terms of function values at points of the discrete subset
. Moreover, if
tends to zero fast enough as
over
, then this function vanishes identically. To prove these results, a special approximation technique is developed. In the last part of the paper, it is proved that, under certain conditions on
and
, which are close to exact conditions, the function
bounded on
is bounded on the ray. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|