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Interpolation, Schur Functions and Moment Problems

Part of the Operator Theory: Advances and Applications Book Series (volume 165)

Editors: Alpay, Daniel; Gohberg, Israel

DOI: 10.1007/3-7643-7547-7

ISBN: 978-3-7643-7546-1

Publisher: Birkhäuser Basel - Springer Journals

Jan 1, 2006

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Chapter 1Basic Boundary Interpolation for Generalized Schur Functions and Factorization of Rational J-unitary Matrix Functions

Alpay, Daniel; Dijksma, Aad; Langer, Heinz; Wanjala, Gerald

Pages: 1 –29

[We define and solve a boundary interpolation problem for generalized Schur functions s(z) on the open unit disk \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs}...
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Chapter 2Discrete Analogs of Canonical Systems with Pseudo-exponential Potential. Inverse Problems

Alpay, Daniel; Gohberg, Israel

Pages: 31 –65

[We study the inverse problems associated to the characteristic spectral functions of first-order discrete systems. We focus on the case where the coefficients defining the discrete system are strictly pseudo-exponential. The arguments use methods from system theory. An important role is played...
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Chapter 3Boundary Nevanlinna—Pick Interpolation Problems for Generalized Schur Functions

Bolotnikov, Vladimir; Kheifets, Alexander

Pages: 67 –119

[Three boundary multipoint Nevanlinna-Pick interpolation problems are formulated for generalized Schur functions. For each problem, the set of all solutions is parametrized in terms of a linear fractional transformation with a Schur class parameter.]
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Chapter 4A Truncated Matricial Moment Problem on a Finite Interval

Choque Rivero, Abdon E.; Dyukarev, Yuriy M.; Fritzsche, Bernd; Kirstein, Bernd

Pages: 121 –173

[The main goal of this paper is to study the truncated matricial moment problem on a finite closed interval by using the FMI method of V.P. Potapov. The solvability of the problem is characterized by the fact that two block Hankel matrices built from the data of the problem are nonnegative...
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Chapter 5Shift Operators Contained in Contractions, Schur Parameters and Pseudocontinuable Schur Functions

Dubovoy, V. K.

Pages: 175 –250

[The main goal of the paper is to study the properties of the Schur parameters of the noninner functions of the Schur class S which admit a pseudocontinuation. To realize this aim we construct a model of completely nonunitary contraction in terms of Schur parameters of its characteristic function...
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Chapter 6The Matricial Carathéodory Problem in Both Nondegenerate and Degenerate Cases

Fritzsche, Bernd; Kirstein, Bernd; Lasarow, Andreas

Pages: 251 –290

[The main goal of this paper is to present a new approach to both the nondegenerate and degenerate case of the matricial Carathéodory problem. This approach is based on the analysis of central matrix-valued Carathéodory functions which was started in [FK1] and then continued in [FK3]. In the...
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Chapter 7A Gohberg-Heinig Type Inversion Formula Involving Hankel Operators

Groenewald, G. J.; Kaashoek, M. A.

Pages: 291 –302

[A Gohberg-Heinig type inversion formula is derived for operators I — K2K1, where K1 and K2 are Hankel integral operators acting between vector-valued L1-spaces over [0,∞]. The main result is first proved, by using linear algebra tools, for the case when the corresponding kernel functions have a...

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