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Operator Theory, Analysis and the State Space Approach

Part of the Operator Theory: Advances and Applications Book Series (volume 271)

Editors: Bart, Harm; ter Horst, Sanne; Ran, André C.M.; Woerdeman, Hugo J.

DOI: 10.1007/978-3-030-04269-1

ISBN: 978-3-030-04268-4

Publisher: Springer International Publishing - Springer Journals

Dec 31, 2018

1 - 10 of 18 Chapters

LitStream

Chapter 1Carathéodory extremal functions on the symmetrized bidisc

Agler, Jim; Lykova, Zinaida A.; Young, N. J.

Pages: 1 –21

[We show how realization theory can be used to find the solutions of the Carathéodory extremal problem on the symmetrized bidisc \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy}...
LitStream

Chapter 2Standard versus strict Bounded Real Lemma with infinite-dimensional state space III: The dichotomous and bicausal cases

Ball, J. A.; Groenewald, G. J.; ter Horst, S.

Pages: 23 –73

[This is the third installment in a series of papers concerning the Bounded Real Lemma for infinite-dimensional discrete-time linear input/state/output systems. In this setting, under appropriate conditions, the lemma characterizes when the transfer function associated with the system has...
LitStream

Chapter 3L-free directed bipartite graphs and echelon-type canonical forms

Bart, Harm; Ehrhardt, Torsten; Silbermann, Bernd

Pages: 75 –117

[It is common knowledge that matrices can be brought in echelon form by Gaussian elimination and that the reduced echelon form of a matrix is canonical in the sense that it is unique. In [4], working within the context of the algebra \documentclass[12pt]{minimal} \usepackage{amsmath}...
LitStream

Chapter 4Extreme individual eigenvalues for a class of large Hessenberg Toeplitz matrices

Bogoya, J. M.; Grudsky, S. M.; Malysheva, I. S.

Pages: 119 –143

[In a previous work we studied the asymptotic behavior of individual inner eigenvalues of the n-by-n truncations of a certain family of infinite Hessenberg Toeplitz matrices as n goes to infinity. In the present work we deal with the extreme eigenvalues. The generating function of the Toeplitz...
LitStream

Chapter 5How to solve an equation with a Toeplitz operator?

Böttcher, Albrecht; Wegert, Elias

Pages: 145 –166

[An equation with a Hardy space Toeplitz operator can be solved by Wiener–Hopf factorization. However, Wiener–Hopf factorization does not work for Bergman space Toeplitz operators. The only way we see to tackle equations with a Toeplitz operator on the Bergman space is to have recourse to...
LitStream

Chapter 6On the maximal ideal space of even quasicontinuous functions on the unit circle

Ehrhardt, Torsten; Zhou, Zheng

Pages: 167 –179

[Let PQC stand for the set of all piecewise quasicontinuous functions on the unit circle, i.e., the smallest closed subalgebra of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy}...
LitStream

Chapter 7Bisection eigenvalue method for Hermitian matrices with quasiseparable representation and a related inverse problem

Eidelman, Y.; Haimovici, I.

Pages: 181 –200

[We study the bisection method for Hermitian matrices with quasiseparable representations.We extend here our results (published in ETNA, 44, 342–366 (2015)) for quasiseparable matrices of order one to an essentially wider class of matrices with quasiseparable representation of any order. To...
LitStream

Chapter 8A note on inner-outer factorization of wide matrix-valued functions

Frazho, A. E.; Ran, A. C. M.

Pages: 201 –214

[In this paper we expand some of the results of [8, 9, 10]. In fact, using the techniques of [8, 9, 10], we provide formulas for the full rank inner-outer factorization of a wide matrix-valued rational function G with H∞ entries, that is, functions G with more columns than rows. State space...
LitStream

Chapter 9An application of the Schur complement to truncated matricial power moment problems

Fritzsche, Bernd; Kirstein, Bernd; Mädler, Conrad

Pages: 215 –238

[The main goal of this paper is to reconsider a phenomenon which was treated in earlier work of the authors’ on several truncated matricial moment problems. Using a special kind of Schur complement we obtain a more transparent insight into the nature of this phenomenon. In particular, a concrete...
LitStream

Chapter 10A Toeplitz-like operator with rational symbol having poles on the unit circle I: Fredholm properties

Groenewald, G. J.; ter Horst, S.; Jaftha, J.; Ran, A. C. M.

Pages: 239 –268

[In this paper a definition is given for an unbounded Toeplitzlike operator with rational symbol which has poles on the unit circle. It is shown that the operator is Fredholm if and only if the symbol has no zeroes on the unit circle, and a formula for the index is given as well. Finally, a...

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