On exponential type entire functions without zeros in the open lower half-plane
Classical Analysis and ODEs
2016-06-28 v1 Complex Variables
Abstract
We obtain sufficient conditions for an exponential type entire function not to have zeros in the open lower half-plane. An exact inequality containing the real and imaginary parts of such functions and their derivatives restricted to the real axis is deduced. A connection is established to the positive definite functions.
Cite
@article{arxiv.1606.08255,
title = {On exponential type entire functions without zeros in the open lower half-plane},
author = {Viktor P. Zastavnyi},
journal= {arXiv preprint arXiv:1606.08255},
year = {2016}
}
Comments
28 pages