Operator Theory and Analysis

The M.A. Kaashoek Anniversary Volume Workshop in Amsterdam, November 12–14, 1997

Inbunden, Engelska, 2001

Av H. Bart, I. Gohberg, A.C.M. Ran, A. C. M. Ran

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This book contains the proceedings of the international workshop organized at the Vrije Universiteit Amsterdam in November 1997 and dedicated to the sixtieth birthday of M.A. Kaashoek, one of the leading experts in operator theory and its applications. The workshop focused on areas in mathematical and functional analysis where the ideas and results of M.A. Kaashoek played an important role. The papers of this volume cover a wide range of topics centered around factorization of matrix valued functions, interpolation theory, and spectral theory. Other papers deal with canonical systems of differential equations, operators in indefinite inner product spaces, and the effect of small delays on stability and control of partial differential equations. The book starts with biographical material and a list of publications of M.A. Kaashoek. The main part consists of original research papers, which contain new interesting results. The book should be of interest to a wide range of readers in pure and applied mathematics and engineering.

Produktinformation

Utgivningsdatum2001-01-01
Mått155 x 235 x 30 mm
Vikt927 g
FormatInbunden
SpråkEngelska
SerieOperator Theory: Advances and Applications
Antal sidor433
Upplaga2001
FörlagBirkhauser Verlag AG
ISBN9783764364991

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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 viaPolynomial 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.- 2. The Matrix Case.- 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. TheSelf-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.