3 research outputs found
Bandlimited approximations to the truncated Gaussian and applications
In this paper we extend the theory of optimal approximations of functions in the -metric by entire functions of prescribed
exponential type (bandlimited functions). We solve this problem for the
truncated and the odd Gaussians using explicit integral representations and
fine properties of truncated theta functions obtained via the maximum principle
for the heat operator. As applications, we recover most of the previously known
examples in the literature and further extend the class of truncated and odd
functions for which this extremal problem can be solved, by integration on the
free parameter and the use of tempered distribution arguments. This is the
counterpart of the work \cite{CLV}, where the case of even functions is
treated.Comment: to appear in Const. Appro
On Local Behavior of Holomorphic Functions Along Complex Submanifolds of C^N
In this paper we establish some general results on local behavior of
holomorphic functions along complex submanifolds of \Co^{N}. As a corollary,
we present multi-dimensional generalizations of an important result of Coman
and Poletsky on Bernstein type inequalities on transcendental curves in
\Co^{2}.Comment: minor changes in the formulation and the proof of Lemma 8.