Operator Theory and Analysis,9783764364991

Operator Theory and Analysis

by ; ; ;
ISBN13: 9783764364991
ISBN10: 3764364998
Format: Hardcover
Pub. Date: 2001-03-01
Publisher(s): Birkhauser
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Summary

Text for readers in pure and applied mathematics and engineering, containing biographical material and a list of publications by M.A. Kaashoek, as well a collection of original research papers from the international workshop held in November 1997 in Kaashoek's honor.

Table of Contents

Preface v
Photograph of M.A. Kaashoek xiii
Curriculum Vitae of M.A. Kaashoek xv
List of Publications of M.A. Kaashoek
xix
Opening Address xxxi
I. Gohberg
Personal Reminiscences xxxv
H. Bart
A.C.M. Ran
H.J. Woerdeman
On the Separation of Certain Spectral Components of Selfadjoint Operator Matrices
1(12)
V. Adamyan
R. Mennicken
Introduction
1(3)
Conditions for the Separation of Spectral Components
4(5)
Example
9(4)
References
11(2)
A Coisometric Realization for Triangular Integral Operators
13(40)
D. Alpay
V. Bolotnikov
A. Dijksma
Y. Peretz
Introduction
13(2)
Preliminaries and Notations
15(8)
Resolvent Operators and Resolvent Equations
23(3)
The State Spaces HL(S) and HR(S)
26(8)
The Coisometric Realization
34(19)
References
51(2)
Some Remarks on the Inverse Monodromy Problem for 2 x 2 Canonical Differential Systems
53(36)
D.Z. Arov
H. Dym
Introduction
53(6)
Monodromy Matrices with Zero Type in the Upper Half Plane
59(7)
Monodromy Matrices with Zero Type in the Lower Half Plane
66(2)
Monodromy Matrices with Nonzero Type in Both Halfplanes
68(3)
Reparametrizations
71(3)
Three Classes of J-inner mvf's and Some Examples
74(9)
Another Parametrization
83(6)
References
86(3)
Interpolation and Commutant Lifting for Multipliers on Reproducing Kernel Hilbert Spaces
89(50)
J.A. Ball
T.T. Trent
V. Vinnikov
Introduction
89(4)
The Multiplier Space for H(kd)
93(10)
Multipliers for Nevanlinna-Pick-type Kernels
103(4)
Interpolation by Multipliers
107(10)
The Commutant Lifting Theorem for Mk (&epsis;, &epsis;*)
117(14)
Examples and Applications
131(8)
References
135(4)
Sums of Idempotents and Logarithmic Residues in Matrix Algebras
139(30)
H. Bart
T. Erhardt
B. Silbermann
Introduction
139(1)
Preliminaries
140(2)
Matrix Algebras Generated by a Single Matrix
142(5)
Rank, Trace and Decomposition of Matrices
147(6)
Logarithmic Residues of Matrix and Fredholm Operator Valued Functions
153(4)
The Algebra of Block Upper Triangular Matrices
157(12)
References
167(2)
Generalized nevanlinna Functions with Polynomial Asymptotic behaviour at Infinity and Regular Perturbations
169(22)
V. Derkach
S. Hassi
H. De Snoo
Introduction
169(3)
Preliminaries
172(3)
Multiplicity of the Generalized Poles for the Sum of Nκ-functions
175(4)
Polynomial Behaviour at Infinity
179(1)
The Subclasses Induced via Polynomial Asymptotics to Nκ, 0
180(4)
Spectral Characterizations of Regular Rank One Perturbations
184(7)
References
188(3)
Extensions of Matrix Valued Inner Products on Modules and the Inversion Formula for Block Toeplitz Matrices
191(38)
R.L. Ellis
I. Gohberg
Introduction
191(1)
The Scalar Case
192(16)
Extension of a Scalar Product
192(4)
Connections with Prediction Theory and the Extension Theorem
196(2)
Properties of the Extended Scalar Product
198(7)
The Inversion Formula
205(3)
The Matrix Case
208(21)
Matrix Valued Inner Products on Modules
208(3)
Extension of a Matrix-valued Inner Product
211(6)
Properties of the Extended Matrix-valued Inner Product
217(7)
The Gohberg-Heinig Formula
224(3)
References
227(2)
Linear Independence of Jordan Chains
229(18)
K.-H. Forster
B. Nagy
Introduction
229(1)
Linearly Independent Chains with Respect to a Sequence of Operators
230(4)
Jordan Chains of Holomorphic Operator Functions
234(8)
Right (spectral) Roots of a Regular Holomorphic Matrix Functions
242(5)
References
244(3)
Weighted nevanlinna-Pick Interpolation
247(28)
A.E. Frazho
Introduction
247(2)
Preliminaries
249(5)
Some State Space Existence Results
254(2)
The Outer Spectral Factor Case
256(5)
A State Space Solution
261(5)
A State Space Computation for B and Bh
266(3)
The Case when T QT* ≤ Q
269(6)
References
273(2)
Effects of Small Delays on Stability and Control
275(28)
J.K. Hale
S.M. Verduyn Lunel
Introduction
275(3)
The Abstract Setting of the Problem
278(4)
Difference Equations
282(11)
Neutral Delay Differential Equations
293(2)
Delayed Boaundary Control in a Hyperbolic Equation
295(8)
References
299(4)
Generalized bezoutian, Factorization of Rational Matrix Functions and Matrix Quadratic Equations
303(20)
I. Karelin
L. Lerer
Introduction
303(2)
Bezoutian of Rational Matrix Functions and Matrix Quadratic Equations
305(6)
Generalized T-Bezoutian of Rational Matrix Functions
311(3)
Discrete Quadratic Equation and Factorizations of Rational Matrix Functions
314(9)
References
320(3)
A Note on Factorization of Analytic Matrix Functions
323(8)
P. Lancaster
A. Markus
Introduction
323(2)
Preliminary Results
325(2)
Spectral Divisors and the Case c(F) = 1
327(1)
When Γ is a Circle
328(3)
References
329(2)
Diagonalization of certain Block Operator Matrices and Applications to Dirac Operators
331(28)
H. Langer
C. Tretter
Introduction
331(2)
Basic Propositions
333(4)
Block Operator Matrices
337(4)
The Self-adjoint Case
341(9)
The Non-self-adjoint Case
350(4)
Dirac Operators with Potential
354(5)
References
357(2)
Stability of Pseudospectral Factorizations
359(26)
A. Ran
L. Rodman
D. Temme
Introduction
359(1)
Dissipative Matrices and their Invariant Subspaces
360(5)
Functions of the Form Identity Plus a Contraction
365(12)
Positive Real Functions
377(8)
References
382(3)
Factorization of Almost Periodic Matrix Functions of Several Variables and Toeplitz Operators
385(32)
L. Rodman
I.M. Spitkovsky
H.Z. Woerdeman
Introduction
385(2)
Algebras of Almost Periodic Functions and Factorizations
387(5)
Toeplitz Operators
392(4)
Factorization of Sectorial Matrix Functions
396(6)
Factorization of Hermitian Matrix Functions
402(3)
One-sided Invertibility of Toeplitz Operators
405(2)
Robustness and Continuity of Factorizations
407(10)
References
413(4)
Simultaneous Similarity of Pairs of Companions to their Transposes
417(10)
R. Zuidwijk
Introduction
417(1)
Companion and Bezoutian Matrices
418(4)
Simultaneous Similarity
422(5)
References
424(3)
Conference Programm 427(4)
List of Participants 431

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