Operator Theory and Analysis: The M.A. Kaashoek Anniversary Volume Workshop in Amsterdam, November 12-14, 1997

ISBN-13: 9783034895026 / Angielski / Miękka / 2012 / 433 str.

H. Bart; I. Gohberg; A. C. M. Ran

Opis

On November 12-14, 1997 a workshop was held at the Vrije Universiteit Amsterdam on the occasion of the sixtieth birthday ofM. A. Kaashoek. The present volume contains the proceedings of this workshop. The workshop was attended by 44 participants from all over the world: partici- pants came from Austria, Belgium, Canada, Germany, Ireland, Israel, Italy, The Netherlands, South Africa, Switzerland, Ukraine and the USA. The atmosphere at the workshop was very warm and friendly. There where 21 plenary lectures, and each lecture was followed by a lively discussion. The workshop was supported by: the Vakgroep Wiskunde of the Vrije Univer- siteit, the department of Mathematics and Computer Science of the Vrije Univer- siteit, the Stichting VU Computer Science & Mathematics Research Centre, the Thomas Stieltjes Institute for Mathematics, and the department of Economics of the Erasmus University Rotterdam. The organizers would like to take this opportunity to express their gratitude for the support. Without it the workshop would not have been so successful as it was. 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 l. Gohberg Opening Address . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxxi H. Bart, A. C. M. Ran and H. I. Woerdeman Personal Reminiscences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxxv V. Adamyan and R. Mennicken On the Separation of Certain Spectral Components of Selfadjoint Operator Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2. Conditions for the Separation of Spectral Components . . . . . . . 4 3. Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Spis treści

On the Separation of Certain Spectral Components of Selfadjoint Operator Matrices.- 1. Introduction.- 2. Conditions for the Separation of Spectral Components.- 3. Example.- References.- A Coisometric Realization for Triangular Integral Operators.- 1. Introduction.- 2. Preliminaries and Notations.- 3. Resolvent Operators and Resolvent Equations.- 4. The State SpacesHL(S) andHR(S).- 5. The Coisometric Realization.- References.- Some Remarks on the Inverse Monodromy Problem for 2 x 2 Canonical Differential Systems.- 1. Introduction.- 2. Monodromy Matrices with Zero Type in the Upper Half Plane.- 3. Monodromy Matrices with Zero Type in the Lower Half Plane.- 4. Monodromy Matrices with Nonzero Type in Both Halfplanes.- 5. Reparametrizations.- 6. Three Classes of J-inner mvf’s and Some Examples.- 7. Another Parametrization.- References.- Interpolation and Commutant Lifting for Multipliers on Reproducing Kernel Hilbert Spaces.- 1. Introduction.- 2. The Multiplier Space forH(kd).- 3. Multipliers for Nevanlinna-Pick-type Kernels.- 4. Interpolation by Multipliers.- 5. The Commutant Lifting Theorem forMk(?,?*).- 6. Examples and Applications.- References.- Sums of Idempotents and Logarithmic Residues in Matrix Algebras.- 1. Introduction.- 2. Preliminaries.- 3. Matrix Algebras Generated by a Single Matrix.- 4 Rank, Trace and Decomposition of Matrices.- 5. Logarithmic Residues of Matrix and Fredholm Operator Valued Functions.- 6. The Algebra of Block Upper Triangular Matrices.- References.- Generalized Nevanlinna Functions with Polynomial Asymptotic Behaviour at Infinity and Regular Perturbations.- 1. Introduction.- 2. Preliminaries.- 3. Multiplicity of the Generalized Poles for the Sum of Nk -functions.- 4. Polynomial Behaviour at Infinity.- 5. The Subclasses Induced via Polynomial Asymptotics to Nk0.- 6. Spectral Characterizations of Regular Rank One Perturbations.- References.- Extensions of Matrix Valued Inner Products on Modules and the Inversion Formula for Block Toeplitz Matrices.- 0. Introduction.- 1. The Scalar Case.- 1.1 Extension of a Scalar Product.- 1.2 Connections with Prediction Theory and the Extension Theorem.- 1.3 Properties of the Extended Scalar Product.- 1.4 The Inversion Formula.- 2. The Matrix Case.- 2.1 Matrix Valued Inner Products on Modules.- 2.2 Extension of a Matrix-valued Inner Product.- 2.3 Properties of the Extended Matrix-valued Inner Product.- 2.4 The Gohberg-Heinig Formula.- References.- Linear Independence of Jordan Chains.- 1. Introduction.- 2. Linearly Independent Chains with Respect to a Sequence of Operators.- 3. Jordan Chains of Holomorphic Operator Functions.- 4. Right (spectral) Roots of a Regular Holomorphic Matrix Function.- References.- Weighted Nevanlinna-Pick Interpolation.- 0. Introduction.- 1. Preliminaries.- 2. Some State Space Existence Results.- 3. The Outer Spectral Factor Case.- 4. A State Space Solution.- 5. A State Space Computation for $$ \tilde B $$ and $$ {\tilde B_h} $$.- 6. The Case whenT QT*?Q.- References.- Effects of Small Delays on Stability and Control.- 1. Introduction.- 2. The Abstract Setting of the Problem.- 3. Difference Equations.- 4. Neutral Delay Differential Equations.- 5. Delayed Boundary Control in a Hyperbolic Equation.- References.- Generalized Bezoutian, Factorization of Rational Matrix Functions and Matrix Quadratic Equations.- 0. Introduction.- 1. Bezoutian of Rational Matrix Functions.- and Matrix Quadratic Equations.- 2. Generalized T-Bezoutian of Rational Matrix Functions.- 3. Discrete Quadratic Equation and Factorizations of Rational Matrix Functions.- References.- A Note on Factorization of Analytic Matrix Functions.- 1. Introduction.- 2. Preliminary Results.- 3. Spectral Divisors and the Casec(F) = 1.- 4. When ? is a Circle.- References.- Diagonalization of certain Block Operator Matrices and Applications to Dirac Operators.- 0. Introduction.- 1. Basic Propositions.- 2. Block Operator Matrices.- 3. The Self-adjoint Case.- 4. The Non—self—adjoint Case.- 5. Dirac Operators with Potential.- References.- Stability of Pseudospectral Factorizations.- 1. Introduction.- 2. Dissipative Matrices and their Invariant Subspaces.- 3. Functions of the Form Identity Plus a Contraction.- 4. Positive Real Functions.- References.- Factorization of Almost Periodic Matrix Functions of Several Variables and Toeplitz Operators.- 1. Introduction.- 2. Algebras of Almost Periodic Functions and Factorizations.- 3. Toeplitz Operators.- 4. Factorization of Sectorial Matrix Functions.- 5. Factorization of Hermitian Matrix Functions.- 6. One-sided Invertibility of Toeplitz Operators.- 7. Robustness and Continuity of Factorizations.- References.- Simultaneous Similarity of Pairs of Companions to their Transposes.- 1. Introduction.- 2. Companion and Bezoutian Matrices.- 3. Simultaneous Similarity.- References.- Conference Programm.- List of Participants.