Inverse problem for zeros of certain Koebe-related functions
type: Item
instance of: scholarly article
title: Inverse problem for zeros of certain Koebe-related functions
zbMATH Open document ID: 0884.30003
DOI: 10.1007/BF02788027
author: Donald Sarason
author: Daniel Suárez
published in: Journal d'Analyse Mathématique
publication date: 1998-03-22T00:00:00Z
review text: The authors consider the zero set of a Koebe type function \(K_{\lambda,\mu}^{(n)}(z)=1-\sum_{k=1}^n \mu_k K(\lambda_k z)\), where \(K\) denotes the Koebe function \(z(1-z)^{-2}\), \(\lambda_k\in{\mathbf C}\), \(|\lambda_k|=1\), \(\mu_k > 0\). The following statement is proved: If \(w_1,\dots, w_n\) is a sequence of nonzero points in the unit disk \({\mathbf D}\), then there is the unique function \(K_{\lambda, \mu}^{(n)}\) such that \(w_1,\dots, w_n\) coincides with the zero set in \({\mathbf D}\) of the function \(K_{\lambda,\mu}^{(n)}\).
Mathematics Subject Classification ID: 30C15
Mathematics Subject Classification ID: 30-02
zbMATH DE Number: 1038443
zbMATH Keywords: Koebe function
zbMATH Keywords: rational function
reviewed by: Saulius Norvidas
MaRDI profile type: Publication
cites work: Errata: Harmonically weighted Dirichlet spaces associated with finitely atomic measures
full work available at URL: https://doi.org/10.1007/bf02788027
OpenAlex ID: W1975261515
description: scientific article; zbMATH DE number 1038443