Cyclicity and Maximal Multiplicity for Zeros of Families of Analytic Functions
Complex Variables
2007-05-23 v1
Abstract
Let f_{\lambda} be a family of holomorphic functions in the unit disk, holomorphic in parameter \lambda\in U\subset\C^{n}. We estimate the number of zeros of f_{\lambda} in a smaller disk via some characteristic of the ideal generated by Taylor coefficients of f_{\lambda}. Our estimate is locally sharp and improve the previous estimate obtained by Roytwarf and Yomdin.
Cite
@article{arxiv.math/0205096,
title = {Cyclicity and Maximal Multiplicity for Zeros of Families of Analytic Functions},
author = {Alexander Brudnyi},
journal= {arXiv preprint arXiv:math/0205096},
year = {2007}
}
Comments
11 pages