Pick-Nevanlinna interpolation theorem and multiplication operators on functional Hilbert spaces
type: Item
instance of: scholarly article
title: Pick-Nevanlinna interpolation theorem and multiplication operators on functional Hilbert spaces
zbMATH Open document ID: 0847.47014
DOI: 10.1007/BF01198940
author: Gadadhar Misra
published in: Integral Equations and Operator Theory
publication date: 1992-09-27T00:00:00Z
review text: In an attempt to understand the curvature inequalities, we were led to some of the topics discussed below. After recalling some of the basic definitions, we discuss the Pick-Nevanlinna Theorem on the disk in section 2. Our main result is that if we replace the Szegö kernel by any other positive kernel the Pick-Nevanlinna interpolation theorem will be false. In section 3, we discuss Abrahamse's generalization of the Pick-Nevanlinna interpolation theorem to a finitely connected domain in \(C\). Finally, in section 4, we prove that it is not possible to establish an analogue of the Pick-Nevanlinna interpolation theorem for the unit ball. In this connection, we wish to point out that, some recent results of Jim Agler overlap with the material in this paper.
Mathematics Subject Classification ID: 47A57
Mathematics Subject Classification ID: 46E20
zbMATH DE Number: 59724
zbMATH Keywords: curvature inequalities
zbMATH Keywords: Pick-Nevanlinna Theorem
zbMATH Keywords: Szegö kernel
zbMATH Keywords: positive kernel
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 59724