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

^*Corresponding author for this work

Systems, Control and Applied Analysis

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

4 Citations (Scopus)

269 Downloads (Pure)

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. (c) 2012 Royal Dutch Mathematical Society (KWG). Published by Elsevier B.V. All rights reserved.

Original language	English
Pages (from-to)	921-969
Number of pages	49
Journal	Indagationes mathematicae-New series
Volume	23
Issue number	4
DOIs	https://doi.org/10.1016/j.indag.2012.08.002
Publication status	Published - Dec-2012

Keywords

Schur transformation
Generalized Schur function
Generalized Nevanlinna function
Meromorphic function
Projective representation
Pontryagin space
Reproducing kernel
Elementary factor
Basic interpolation problem
Basic boundary interpolation problem
Linear fractional transformation
REPRODUCING KERNEL SPACES
BOUNDARY INTERPOLATION
NEVANLINNA FUNCTIONS
MATRIX FUNCTIONS
OPERATORS
REPRESENTATIONS
POLYNOMIALS

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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. (c) 2012 Royal Dutch Mathematical Society (KWG). Published by Elsevier B.V. All rights reserved.",

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author = "Daniel Alpay and Aad Dijksma and Heinz Langer and Dan Volok",

note = "Relation: http://www.rug.nl/research/jbi/ Rights: University of Groningen, Johann Bernoulli Institute for Mathematics and Computer Science",

year = "2012",

month = dec,

doi = "10.1016/j.indag.2012.08.002",

language = "English",

volume = "23",

pages = "921--969",

journal = "Indagationes mathematicae-New series",

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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

N1 - Relation: http://www.rug.nl/research/jbi/ Rights: University of Groningen, Johann Bernoulli Institute for Mathematics and Computer Science

PY - 2012/12

Y1 - 2012/12

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. (c) 2012 Royal Dutch Mathematical Society (KWG). Published by Elsevier B.V. All rights reserved.

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. (c) 2012 Royal Dutch Mathematical Society (KWG). Published by Elsevier B.V. All rights reserved.

KW - Schur transformation

KW - Generalized Schur function

KW - Generalized Nevanlinna function

KW - Meromorphic function

KW - Projective representation

KW - Pontryagin space

KW - Reproducing kernel

KW - Elementary factor

KW - Basic interpolation problem

KW - Basic boundary interpolation problem

KW - Linear fractional transformation

KW - REPRODUCING KERNEL SPACES

KW - BOUNDARY INTERPOLATION

KW - NEVANLINNA FUNCTIONS

KW - MATRIX FUNCTIONS

KW - OPERATORS

KW - REPRESENTATIONS

KW - POLYNOMIALS

U2 - 10.1016/j.indag.2012.08.002

DO - 10.1016/j.indag.2012.08.002

M3 - Article

SN - 0019-3577

VL - 23

SP - 921

EP - 969

JO - Indagationes mathematicae-New series

JF - Indagationes mathematicae-New series

IS - 4

ER -

A Schur transformation for functions in a general class of domains

Abstract

Keywords

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