Operator Theory and Complex Analysis

Inhaltsverzeichnis

• Scattering matrices for microschemes.
• 1. General expressions for the scattering matrix.
• 2. Continuity condition.
• References.
• Holomorphic operators between Krein spaces and the number of squares of associated kernels.
• 0. Introduction.
• 1. Realizations of a class of Schur functions.
• 2. Positive squares and injectivity.
• 3. Application of the Potapov-Ginzburg transform.
• On reproducing kernel spaces, the Schur algorithm, and interpolation in a general class of domains.
• 1. Introduction.
• 2. Preliminaries.
• 3. B(X) spaces.
• 4. Recursive extractions and the Schur algorithm.
• 5. H?(S) spaces.
• 6. Linear fractional transformations.
• 7. One sided interpolation.
• 8. References.
• The central method for positive semi-definite, contractive and strong Parrott type completion problems.
• 2. Positive semi-definite completions.
• 3. Contractive completions.
• 4. Linearly constrained contractive completions.
• Interpolation by rational matrix functions and stability of feedback systems: The 4-block case.
• 1. Preliminaries.
• 2. A homogeneous interpolation problem.
• 3. Interpolation problem.
• 4. Parametrization of solutions.
• 5. Interpolation and internally stable feedback systems.
• Matricial coupling and equivalence after extension.
• 2. Coupling versus equivalence.
• 3. Examples.
• 4. Special classes of operators.
• Operator means and the relative operator entropy.
• 2. Origins of operator means.
• 3. Operator means and operator monotone functions.
• 4. Operator concave functions and Jensen’s inequality.
• 5. Relative operator entropy.
• An application of Furuta’s inequality to Ando’s theorem.
• 2. Operator functions.
• 3. Furuta’s type inequalities.
• 4. An application to Ando’s theorem.
• Applications of order preserving operator inequalities.
• 1. Application to the relative operator entropy.
• 2. Application to some extended result of Ando’s one.
• The band extension of the real line as a limit of discrete band extensions, I. The main limit theorem.
• I. Preliminaries and preparations.
• II. Band extensions.
• III. Continuous versus discrete.
• Interpolating sequences in the maximal ideal space of H? II.
• 2. Condition (A2).
• 3. Condition (A3).
• 4. Condition (A1).
• Operator matrices with chordal inverse patterns.
• 2. Entry formulae.
• 3. Inertia formula.
• Models and unitary equivalence of cyclic selfadjoint operators in Pontrjagin spaces.
• 1. The class F of linear functionals.
• 2. The Pontrjagin space associated with ? ? F.
• 3. Models for cyclic selfadjoint operators in Pontrjagin spaces.
• 4. Unitary equivalence of cyclic selfadjoint operators in Pontrjagin spaces.
• The von Neumann inequality and dilation theorems for contractions.
• 1. The von Neumann inequality and strong unitary dilation.
• 2. Canonical representation of completely contractive maps.
• 3. An effect of generation of nuclear algebras.
• Interpolation problems, inverse spectral problems and nonlinear equations.
• Extended interpolation problem in finitely connected domains.
• I. Matrices and transformation formulas.
• II. Disc Cases.
• III. Domains of finite connectivity.
• Accretive extensions and problems on the Stieltjes operator-valued functions relations.
• 1. Accretive and sectorial extensions of the positive operators, operators of the class C(?) and theirparametric representation.
• 2. Stieltjes operator-valued functions and their realization.
• 3. M. S. Livsic triangular model of the M-accretive extensions (with real spectrum) of the positive operators.
• 4. Canonical and generalized resolvents of QSC-extensions of Hermitian contractions.
• Commuting nonselfadjoint operators and algebraic curves.
• 1. Commuting nonselfadjoint operators and the discriminant curve.
• 2. Determinantal representations of real plane curves.
• 3. Commutative operator colligations.
• 4. Construction of triangular models: Finite-dimensional case.
• 5. Construction of triangular models: General case.
• 6. Characteristic functions and the factorization theorem.
• All (?) about quasinormal operators.
• 2. Representations.
• 3. Spectrum and multiplicity.
• 4. Special classes.
• 5. Invariant subspaces.
• 6. Commutant.
• 7. Similarity.
• 8. Quasisimilarity.
• 9. Compact perturbation.
• 10. Open problems.
• Workshop Program.
• List of Participants.