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Graphs of zeros of analytic families

Authors:	Alexander Brudnyi

Institution:	Department of Mathematics and Statistics, University of Calgary, Calgary, Alberta, Canada T2N 1N4

Abstract:	Let $\mathcal{F}:=\{f_{\lambda}\}$ be a family of holomorphic functions in a domain $D\subset\mathbb{C}$ depending holomorphically on $\lambda\in U\subset\mathbb{C}^{n}$ . We study the distribution of zeros of $\{f_{\lambda}\}$ in a subdomain $R\subset\subset D$ whose boundary is a closed non-singular analytic curve. As an application, we obtain several results about distributions of zeros of families of generalized exponential polynomials and displacement maps related to certain ODE's.

Keywords:	Graph of zeros exponential polynomial displacement map

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