Approximations of zeros of entire functions by zeros of polynomials
type: Item
instance of: scholarly article
title: Approximations of zeros of entire functions by zeros of polynomials
zbMATH Open document ID: 0963.41007
published in: Journal of Approximation Theory
publication date: 2001-06-17T00:00:00Z
review text: Let \[ f(\lambda):=\sum_{k=0}^{\infty}\frac{a_k\lambda^k}{(k!)^{\rho}}\quad (\lambda \in \mathbb C, a_0=1, \rho >1/2) \] denote an entire function. Set \[ p_n(\lambda):=\sum_{k=0}^{n}\frac{a_k\lambda^k}{(k!)^{\rho}}\quad \text{and}\quad q_n:=\left (\sum_{k=n+1}^{\infty}|a_k|^2\right)^{1/2}. \] In the paper under review, the author proposes a new approach to the following question. If \(q_n\) is small, how close are the zeros of \(p_n\) to the zeros of \(f\)? The author's approach is based on recent estimates for the norm of the resolvent of a Hilbert--Schmidt operator.
reviewed by: George Csordas
Mathematics Subject Classification ID: 41A10
zbMATH DE Number: 1538245
zbMATH Keywords: entire functions
zbMATH Keywords: zeros
zbMATH Keywords: approximations by polynomials
author: Michael I. Gil'
MaRDI profile type: Publication
full work available at URL: jath.2000.3468
OpenAlex ID: W2084410275
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DOI: 10.1006/JATH.2000.3468
description: scientific article; zbMATH DE number 1538245