Recent Advances in Operator Theory

1. Front Matter

   Pages i-lvii

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2. On the Spectral Theory of Degenerate Quadratic Operator Pencils

   • Vadim Adamyan, Reinhard Mennicken, Vjacheslav Pivovarchik

   Pages 1-19

3. Two-sided Tangential Interpolation for Hilbert-Schmidt Operator Functions on Polydisks

   • Daniel Alpay, Vladimir Bolotnikov, Leiba Rodman

   Pages 21-62

4. Nonstationary Analogs of the Herglotz Representation Theorem: Realizations Centered at an Arbitrary Point

   • D. Alpay, A. Dijksma, Y. Peretz

   Pages 63-87

5. Characteristic Functions of Maximal Sectorial Operators

   • Yury Arlinskii

   Pages 89-108

6. Similarity between Kreĭn Space Bicontractions and Hilbert Space Contractions

   • T. Ya. Azizov, A. I. Barsukov, A. Dijksma, P. Jonas

   Pages 109-129

7. Classification of Cyclic Invariant Subspaces of Jordan Operators

   • Hari Bercovici, Thomas Smotzer

   Pages 131-143

8. Elliptic Spectral Problems of Higher Order with Eigenparameter Dependent Boundary Conditions

   • Paul Binding, Rostyslav Hryniv

   Pages 145-153

9. About Scattering on the Ring

   • V. B. Bogevolnov, A. B. Mikhailova, B. S. Pavlov, A. M. Yafyasov

   Pages 155-173

10. Dilation of Generalized Toeplitz Kernels on Lexicographic Γ × ℝ

    • Ramón Bruzual, Marisela Domínguez

    Pages 175-187

11. On Riccati Equations and Reproducing Kernel Spaces

    • Harry Dym

    Pages 189-215

12. A Status Report on the Asymptotic Behavior of Toeplitz Determinants with Fisher-Hartwig Singularities

    • Torsten Ehrhardt

    Pages 217-241

13. On the Spectrum of Unbounded Off-diagonal 2 × 2 Operator Matrices in Banach Spaces

    • Volker Hardt, Reinhard Mennicken

    Pages 243-266

14. Multithreshold Spectral Phase Transitions for a Class of Jacobi Matrices

    • J. Janas, S. Naboko

    Pages 267-285

15. Positive Extensions and Diagonally Connected Patterns

    • M. A. Kaashoek, H. J. Woerdeman

    Pages 287-305

16. Parametrized Furuta Inequality and its Application

    • Eizaburo Kamei

    Pages 307-317

17. J-Symmetric Factorizations and Algebraic Riccati Equations

    • I. Karelin, L. Lerer, A. C. M. Ran

    Pages 319-360

18. Scattering of Waves by Periodic Gratings and Factorization Problems

    • A. G. Kostyuchenko, A. A. Shkalikov

    Pages 361-383

19. Corners of Numerical Ranges

    • Heinz Langer, Alexander Markus, Christiane Tretter

    Pages 385-400

20. On Some Classes of Extensions of Sectorial Operators and Dual Pairs of Contractions

    • M. M. Malamud

    Pages 401-449

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.

• Hilbert space
• differential operator
• harmonic analysis
• interpolation
• operator
• operator theory
• spectral theory

• Department of Mathematics, University of Groningen, Groningen, The Netherlands

  A. Dijksma

• Division of Mathematics and Computer Science Faculty of Sciences, Vrije Universiteit, Amsterdam, The Netherlands

  M. A. Kaashoek, A. C. M. Ran

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