Carathéodory-Fejér interpolation on polydisks
type: Item
instance of: scholarly article
title: Carathéodory-Fejér interpolation on polydisks
zbMATH Open document ID: 0953.41024
author: Jörg Eschmeier
author: Mihai Putinar
author: Linda J. Patton
published in: Mathematical Research Letters
publication date: 2000-08-13T00:00:00Z
review text: The Carathéodory-Fejér problem consists of the question of whether a polynomial can be extended with higher degree terms to a convergent series from the unit disc into itself. The solvability of this problem is equivalent to the positive semi-definiteness of an associated Toeplitz type matrix which depends only on the coefficients of the original polynomial. In this note the authors propose a solution to the Carathéodory-Fejér problem in the bidisk via Agler's version of the Herglotz-Nevanlinna formula.
Mathematics Subject Classification ID: 41A99
Mathematics Subject Classification ID: 32E99
Mathematics Subject Classification ID: 47A57
zbMATH DE Number: 1489550
zbMATH Keywords: Carathéodory-Fejer problem
zbMATH Keywords: Toeplitz type matrix
zbMATH Keywords: Carathéodory-Fejér problem
zbMATH Keywords: Herglotz-Nevanlinna formula
reviewed by: G. Kohr
MaRDI profile type: Publication
DOI: 10.4310/MRL.2000.V7.N1.A3
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description: scientific article; zbMATH DE number 1489550