Compact Hankel forms on planar domains
type: Item
instance of: scholarly article
title: Compact Hankel forms on planar domains
zbMATH Open document ID: 1181.41022
author: Vasiliy A. Prokhorov
author: Mihai Putinar
published in: Complex Analysis and Operator Theory
publication date: 2009-09-18T00:00:00Z
review text: This paper is devoted to unify some basic questions in the theory of meromorphic approximation in the planar open set \(G\) which supports the Borel measure \(\mu\). To this end the authors start from the abstract theory of bilinear symmetric Hankel form defined on a complex separable Hilbert space \([.,.]\) satisfying \([fx,y]=[x,fy]\). The singular numbers (defined in Adamyan-Arov-Krein theorem) associated to Hankel operators with Markov functions as symbols, doubly orthogonal systems of analytic functions and Hadamard type determinants are investigated. The transition from Hardy space to the Bergman space associated to \(G\) is considered as well as the spectral theory of the Friedrichs operator of the domain \(G\) which leads to some qualitative features of the measure \(\mu\). A precise historical introduction related to the classical approximation theory questions concerned in this paper preceeds the abstract framework.
reviewed by: Jacek Gilewicz
Mathematics Subject Classification ID: 41A20
Mathematics Subject Classification ID: 30E10
Mathematics Subject Classification ID: 47B35
zbMATH DE Number: 5604857
zbMATH Keywords: bilinear symmetric form
zbMATH Keywords: singular numbers
zbMATH Keywords: meromorphic approximation
zbMATH Keywords: rational approximation
MaRDI profile type: Publication
full work available at URL: s11785-008-0094-6
OpenAlex ID: W2005883303
DOI: 10.1007/S11785-008-0094-6
description: scientific article; zbMATH DE number 5604857