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Transactions of the American Mathematical Society

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Graphs of zeros of analytic families


Author: Alexander Brudnyi
Journal: Trans. Amer. Math. Soc. 357 (2005), 1859-1875
MSC (2000): Primary 30C15; Secondary 34C07, 05C99
DOI: https://doi.org/10.1090/S0002-9947-04-03615-3
Published electronically: September 23, 2004
MathSciNet review: 2115079
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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.


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Additional Information

Alexander Brudnyi
Affiliation: Department of Mathematics and Statistics, University of Calgary, Calgary, Alberta, Canada T2N 1N4

DOI: https://doi.org/10.1090/S0002-9947-04-03615-3
Keywords: Graph of zeros, exponential polynomial, displacement map
Received by editor(s): August 7, 2003
Published electronically: September 23, 2004
Additional Notes: The author’s research was supported in part by NSERC
Article copyright: © Copyright 2004 American Mathematical Society

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