Relations between growth of entire functions and behavior of its Taylor coefficients
Complex Variables
2021-02-17 v1
Abstract
We derive in the closed and unimprovable form the bilateral non-asymptotic relations between growth of entire functions and decay rate at infinity of its Taylor coefficients. We investigate the functions of one as well as of several complex variables. We will apply the convex analysis: Young-Fenchel (Legendre) transform, Young inequality, saddle-point method etc.
Keywords
Cite
@article{arxiv.2102.07863,
title = {Relations between growth of entire functions and behavior of its Taylor coefficients},
author = {M. R. Formica and E. Ostrovsky and L. Sirota},
journal= {arXiv preprint arXiv:2102.07863},
year = {2021}
}