Operator Theory and Analysis

, by M. A. Kaashoek Anniversary Volume Workshop; Bart, H.; Gohberg, I.; Ran, A. C. M.

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ISBN: 9783764364991 | 3764364998
Cover: Hardcover
Copyright: 3/1/2001

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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.

Preface

Photograph of M.A. Kaashoek

xiii

Curriculum Vitae of M.A. Kaashoek

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

(12)

V. Adamyan

R. Mennicken

Introduction

(3)

Conditions for the Separation of Spectral Components

(5)

Example

(4)

References

(2)

A Coisometric Realization for Triangular Integral Operators

(40)

D. Alpay

V. Bolotnikov

A. Dijksma

Y. Peretz

Introduction

(2)

Preliminaries and Notations

(8)

Resolvent Operators and Resolvent Equations

(3)

The State Spaces HL(S) and HR(S)

(8)

The Coisometric Realization

(19)

References

(2)

Some Remarks on the Inverse Monodromy Problem for 2 x 2 Canonical Differential Systems

(36)

D.Z. Arov

H. Dym

Introduction

(6)

Monodromy Matrices with Zero Type in the Upper Half Plane

(7)

Monodromy Matrices with Zero Type in the Lower Half Plane

(2)

Monodromy Matrices with Nonzero Type in Both Halfplanes

(3)

Reparametrizations

(3)

Three Classes of J-inner mvf's and Some Examples

(9)

Another Parametrization

(6)

References

(3)

Interpolation and Commutant Lifting for Multipliers on Reproducing Kernel Hilbert Spaces

(50)

J.A. Ball

T.T. Trent

V. Vinnikov

Introduction

(4)

The Multiplier Space for H(kd)

(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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Operator Theory and Analysis

Summary

Table of Contents

Supplemental Materials