A Schur transformation for functions in a general class of domains

Daniel Alpay; Aad Dijksma; Heinz Langer; Dan Volok

doi:10.1016/j.indag.2012.08.002

A Schur transformation for functions in a general class of domains

Daniel Alpay, Aad Dijksma, Heinz Langer, Dan Volok

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

4 Scopus citations

Abstract

In this paper we present a framework in which the Schur transformation and the basic interpolation problem for generalized Schur functions, generalized Nevanlinna functions and the like can be studied in a unified way. The basic object is a general class of functions for which a certain kernel has a finite number of negative squares. The results are based on and generalize those in previous papers of the first three authors on the Schur transformation in an indefinite setting.

Original language	English
Pages (from-to)	921-969
Number of pages	49
Journal	Indagationes Mathematicae
Volume	23
Issue number	4
DOIs	https://doi.org/10.1016/j.indag.2012.08.002
State	Published - 1 Dec 2012
Externally published	Yes

Keywords

Basic boundary interpolation problem
Basic interpolation problem
Elementary factor
Generalized Nevanlinna function
Generalized Schur function
Linear fractional transformation
Meromorphic function
Pontryagin space
Projective representation
Reproducing kernel
Schur transformation

ASJC Scopus subject areas

General Mathematics

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10.1016/j.indag.2012.08.002

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title = "A Schur transformation for functions in a general class of domains",

abstract = "In this paper we present a framework in which the Schur transformation and the basic interpolation problem for generalized Schur functions, generalized Nevanlinna functions and the like can be studied in a unified way. The basic object is a general class of functions for which a certain kernel has a finite number of negative squares. The results are based on and generalize those in previous papers of the first three authors on the Schur transformation in an indefinite setting.",

keywords = "Basic boundary interpolation problem, Basic interpolation problem, Elementary factor, Generalized Nevanlinna function, Generalized Schur function, Linear fractional transformation, Meromorphic function, Pontryagin space, Projective representation, Reproducing kernel, Schur transformation",

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T1 - A Schur transformation for functions in a general class of domains

AU - Alpay, Daniel

AU - Dijksma, Aad

AU - Langer, Heinz

AU - Volok, Dan

PY - 2012/12/1

Y1 - 2012/12/1

N2 - In this paper we present a framework in which the Schur transformation and the basic interpolation problem for generalized Schur functions, generalized Nevanlinna functions and the like can be studied in a unified way. The basic object is a general class of functions for which a certain kernel has a finite number of negative squares. The results are based on and generalize those in previous papers of the first three authors on the Schur transformation in an indefinite setting.

AB - In this paper we present a framework in which the Schur transformation and the basic interpolation problem for generalized Schur functions, generalized Nevanlinna functions and the like can be studied in a unified way. The basic object is a general class of functions for which a certain kernel has a finite number of negative squares. The results are based on and generalize those in previous papers of the first three authors on the Schur transformation in an indefinite setting.

KW - Basic boundary interpolation problem

KW - Basic interpolation problem

KW - Elementary factor

KW - Generalized Nevanlinna function

KW - Generalized Schur function

KW - Linear fractional transformation

KW - Meromorphic function

KW - Pontryagin space

KW - Projective representation

KW - Reproducing kernel

KW - Schur transformation

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DO - 10.1016/j.indag.2012.08.002

M3 - Article

AN - SCOPUS:84870723926

SN - 0019-3577

VL - 23

SP - 921

EP - 969

JO - Indagationes Mathematicae

JF - Indagationes Mathematicae

IS - 4

ER -

A Schur transformation for functions in a general class of domains

Abstract

Keywords

ASJC Scopus subject areas

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