Recent Advances in Operator Theory: The Israel Gohberg Anniversary Volume International Workshop in Groningen, June 1998

✍ Scribed by Vadim Adamyan, Reinhard Mennicken (auth.), A. Dijksma, M. A. Kaashoek, A. C. M. Ran (eds.)

• Publisher: Birkhäuser Basel
• Year: 2001
• Tongue: English
• Leaves: 591
• Series: Operator Theory: Advances and Applications 124
• Edition: 1
• Category: Library

✦ Synopsis

This volume contains a selection of papers in modern operator theory and its applications. Most of them are directly related to lectures presented at the Inter­ national Workshop on Operator Theory and its Applications held at the University of Groningen (IWOTA-98) in Groningen, the Netherlands, from June 30-July 3, 1998. The workshop was attended by 97 mathematicians-of which 12 were PhD or postdoctoral students-from 19 countries. The program consisted of 19 plenary lectures of 40 minutes and 72 lectures of 30 minutes in 4 parallell sessions. The present volume reflects the wide range and rich variety of topics presented and discussed at the workshop. The papers deal with operator polynomials and analytic operator functions, with spectral problems of (partial) differential oper­ ators and related operator matrices, with interpolation, completion and extension problems, with commutant lifting and dilation, with Ricatti equations and real­ ization problems, with scattering theory, with problems from harmonic analysis, and with topics in the theory of reproducing kernel spaces and of spaces with an indefinite metric. All papers underwent the usual refereeing process.

✦ Table of Contents

Front Matter....Pages i-lvii
On the Spectral Theory of Degenerate Quadratic Operator Pencils....Pages 1-19
Two-sided Tangential Interpolation for Hilbert-Schmidt Operator Functions on Polydisks....Pages 21-62
Nonstationary Analogs of the Herglotz Representation Theorem: Realizations Centered at an Arbitrary Point....Pages 63-87
Characteristic Functions of Maximal Sectorial Operators....Pages 89-108
Similarity between Kreĭn Space Bicontractions and Hilbert Space Contractions....Pages 109-129
Classification of Cyclic Invariant Subspaces of Jordan Operators....Pages 131-143
Elliptic Spectral Problems of Higher Order with Eigenparameter Dependent Boundary Conditions....Pages 145-153
About Scattering on the Ring....Pages 155-173
Dilation of Generalized Toeplitz Kernels on Lexicographic Γ × ℝ....Pages 175-187
On Riccati Equations and Reproducing Kernel Spaces....Pages 189-215
A Status Report on the Asymptotic Behavior of Toeplitz Determinants with Fisher-Hartwig Singularities....Pages 217-241
On the Spectrum of Unbounded Off-diagonal 2 × 2 Operator Matrices in Banach Spaces....Pages 243-266
Multithreshold Spectral Phase Transitions for a Class of Jacobi Matrices....Pages 267-285
Positive Extensions and Diagonally Connected Patterns....Pages 287-305
Parametrized Furuta Inequality and its Application....Pages 307-317
J -Symmetric Factorizations and Algebraic Riccati Equations....Pages 319-360
Scattering of Waves by Periodic Gratings and Factorization Problems....Pages 361-383
Corners of Numerical Ranges....Pages 385-400
On Some Classes of Extensions of Sectorial Operators and Dual Pairs of Contractions....Pages 401-449
Liftings of Intertwining Operators....Pages 451-471
Some Estimates for the Resolvent and for the Lengths of Jordan Chains of an Analytic Operator Function....Pages 473-479
The Parrott Problem for Singular Values....Pages 481-503
Unconditional Decompositions and Schur-type Multipliers....Pages 505-525
Scattering in a Loop-shaped Waveguide....Pages 527-543
Pseudospectra of Operator Polynomials....Pages 545-558

✦ Subjects

Mathematics, general