Notes on interpolation in the generalized schur class. II. Nudel'man's problem

D. Alpay; T. Constantinescu; A. Dijksma; J. Rovnyak

doi:10.1090/s0002-9947-02-03148-3

Notes on interpolation in the generalized schur class. II. Nudel'man's problem

D. Alpay, T. Constantinescu, A. Dijksma, J. Rovnyak

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

An indefinite generalization of Nudel'man's problem is used in a systematic approach to interpolation theorems for generalized Schur and Nevanlinna functions with interior and boundary data. Besides known results on existence criteria for Pick-Nevanlinna and Carathéodory-Fejér interpolation, the method yields new results on generalized interpolation in the sense of Sarason and boundary interpolation, including properties of the finite Hubert transform relative to weights. The main theorem appeals to the Ball and Helton almost-commutant lifting theorem to provide criteria for the existence of a solution to Nudel'man's problem.

Original language	English
Pages (from-to)	813-836
Number of pages	24
Journal	Transactions of the American Mathematical Society
Volume	355
Issue number	2
DOIs	https://doi.org/10.1090/s0002-9947-02-03148-3
State	Published - 1 Jan 2003
Externally published	Yes

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1090/s0002-9947-02-03148-3

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abstract = "An indefinite generalization of Nudel'man's problem is used in a systematic approach to interpolation theorems for generalized Schur and Nevanlinna functions with interior and boundary data. Besides known results on existence criteria for Pick-Nevanlinna and Carath{\'e}odory-Fej{\'e}r interpolation, the method yields new results on generalized interpolation in the sense of Sarason and boundary interpolation, including properties of the finite Hubert transform relative to weights. The main theorem appeals to the Ball and Helton almost-commutant lifting theorem to provide criteria for the existence of a solution to Nudel'man's problem.",

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N2 - An indefinite generalization of Nudel'man's problem is used in a systematic approach to interpolation theorems for generalized Schur and Nevanlinna functions with interior and boundary data. Besides known results on existence criteria for Pick-Nevanlinna and Carathéodory-Fejér interpolation, the method yields new results on generalized interpolation in the sense of Sarason and boundary interpolation, including properties of the finite Hubert transform relative to weights. The main theorem appeals to the Ball and Helton almost-commutant lifting theorem to provide criteria for the existence of a solution to Nudel'man's problem.

AB - An indefinite generalization of Nudel'man's problem is used in a systematic approach to interpolation theorems for generalized Schur and Nevanlinna functions with interior and boundary data. Besides known results on existence criteria for Pick-Nevanlinna and Carathéodory-Fejér interpolation, the method yields new results on generalized interpolation in the sense of Sarason and boundary interpolation, including properties of the finite Hubert transform relative to weights. The main theorem appeals to the Ball and Helton almost-commutant lifting theorem to provide criteria for the existence of a solution to Nudel'man's problem.

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Notes on interpolation in the generalized schur class. II. Nudel'man's problem

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