Nevanlinna-Pick interpolation with boundary data
type: Item
instance of: scholarly article
title: Nevanlinna-Pick interpolation with boundary data
zbMATH Open document ID: 0906.30031
DOI: 10.1007/BF01238220
author: Donald Sarason
published in: Integral Equations and Operator Theory
publication date: 1999-02-22T00:00:00Z
review text: Versions of the Nevanlinna-Pick interpolation problems (\textit{C. R. Nevanlinna} [Ann. Acad. Sci. Fennicae (A) 13, No. 1, 1-17 (1916; JFM 47.0271.02)], in which the interpolation nodes are on \(\partial D\), the unit circle, and the interpolation values on the boundary of the allowed region, are studied. The solvability criterion of the problem is found for interpolating functions in the Carathéodory class \(C\) and for functions in the Schur class \(S\). A nonempty problem solution set for \((\partial NPC)\), \((\partial NPC)'\) depends on the Pick matrix (whether it is positive, semidefinite and saturated). Similar relations are valid for \((\partial NPS)\) and \((\partial NPS)'\).
Mathematics Subject Classification ID: 30E05
Mathematics Subject Classification ID: 47A57
zbMATH DE Number: 1129333
zbMATH Keywords: moment problems
zbMATH Keywords: operator methods in interpolation
zbMATH Keywords: JFM 47.0271.02
zbMATH Keywords: Carathéodory class
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1129333