Linear analysis of quadrature domains. II
type: Item
instance of: scholarly article
title: Linear analysis of quadrature domains. II
zbMATH Open document ID: 0968.30016
DOI: 10.1007/BF02810668
author: Björn Gustafsson
author: Mihai Putinar
published in: Israel Journal of Mathematics
publication date: 2001-05-01T00:00:00Z
review text: A bounded domain \(\Omega\) in the complex plane is called a quadrature domain if a distribution \(u\) with finite support in \(\Omega\) exists so that \(\int_\Omega fdA=u(f)\) for all \(f\) holomorphic and integrable in \(\Omega\), where \(A\) denotes the two-dimensional Lebesgue measure. The paper is a continuation of a work of \textit{M. Putinar} [Ark. Mat. 33, No. 2, 357-376 (1995; Zbl 0892.47025)] and is devoted to some constructive aspects of the relation between quadrature domains and their linear data. The first sections are concerned with formulas for the moments \(\int_\Omega z^m\overline z^n dA(z)\) of the domain, where the defining polynomial of \(\Omega\) is assumed to be given. The further sections of the paper deal with some properties of the resolvent of the linear data of a quadrature domain. Finally, explicit computations of order-two quadrature domains illustrate the main results.
Mathematics Subject Classification ID: 30E05
zbMATH DE Number: 1558324
zbMATH Keywords: quadrature domain
reviewed by: Jürgen Müller
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1558324