Spectral Theory in Inner Product Spaces and Applications: 6th Workshop on Operator Theory in Krein Spaces and Operator Polynomials, Berlin, December 2006 (Operator Theory: Advances and Applications)

This book contains a collection of recent research papers originating from the 6th Workshop on Operator Theory in Krein Spaces and Operator Polynomials, which was held at the TU Berlin, Germany, December 14 to 17, 2006. The contributions in this volume are devoted to spectral and perturbation theory of linear operators in spaces with an inner product, generalized Nevanlinna functions and problems and applications in the field of differential equations. Among the discussed topics are linear relations, singular perturbations, de Branges spaces, nonnegative matrices and abstract kinetic equations. Lectures held at the 6th Workshop on Operator Theory in Krein Spaces --After dinner speech on the inventor of the equality sign /A. Dijksma --Speech on the occasion of the retirement of Peter Jonas /H. Langer --Augmented Schur parameters for generalized Nevanlinna functions and approximation /D. Alpay, A. Dijksma and H. Langer --On domains of powers of linear operators and finite rank perturbations /T. Ya. Azizov ... [et al.] --Finite-dimensional de Branges subspaces generated by majorants /A. Baranov and H. Woracek --Trace formulae for dissipative and coupled scattering systems /J. Behrndt, M.M. Malamud and H. Neidhardt --Approximation of N[superscript infinity symbol, subscript k]-functions I: models and regularization /A. Dijksma, A. Luger and Y. Shondin --On the block numerical range of nonnegative matrices /K.H. Förster and N. Hartanto --A quantum dot with impurity in the Lobachevsky plane /V. Geyler, P. Šťovíček and M. Tušek --One-dimensional perturbations, asymptotic expansions, and spectral gaps /S. Hassi, A. Sandovici H.S.V. de Snoo and H. Winkler --Abstract kinetic equations with positive collision operators /I.M. Karabash --On the structure of semigroups of operators acting in spaces with indefinite metric /V.A. Khatskevich and V.A. Senderov --G-self-adjoint operators in almost Pontryagin spaces /F. Philipp and C. Trunk --On a Kreĭn criterion /A. Sandovici --Two-sided weighted shifts are "almost Krein" normal /F.H. Szafraniec 3764389109......Page 1 Operator Theory: Advances and Applications Vol. 188......Page 3 Spectral Theory in Inner Product Spaces and Applications......Page 4 Contents......Page 6 Preface......Page 8 After Dinner Speech on the Inventor of the Equality Sign......Page 12 Speech on the Occasion of the Retirement of Peter Jonas......Page 15 Augmented Schur Parameters for Generalized Nevanlinna Functions and Approximation......Page 19 On Domains of Powers of Linear Operators and Finite Rank Perturbations......Page 49 Finite-dimensional de Branges Subspaces Generated by Majorants......Page 55 Trace Formulae for Dissipative and Coupled Scattering Systems......Page 67 Approximation of N∞ κ -functions I: Models and Regularization......Page 104 On the Block Numerical Range of Nonnegative Matrices......Page 130 A Quantum Dot with Impurity in the Lobachevsky Plane......Page 151 One-dimensional Perturbations, Asymptotic Expansions, and Spectral Gaps......Page 165 Abstract Kinetic Equations with Positive Collision Operators......Page 190 On the Structure of Semigroups of Operators Acting in Spaces with Indefinite Metric......Page 211 G-Self-adjoint Operators in Almost Pontryagin Spaces......Page 220 On a Kreın Criterion......Page 249 Two-sided Weighted Shifts Are ‘Almost Krein’ Normal......Page 256