Operator Theory and Boundary Eigenvalue Problems

Coisometrically valued rational matrix functions.- 1. Introduction.- 2. Functions with coisometric values on the line.- 3. Functions with coisometric values on the circle.- 4. Inner functions.- References.- On some aspects of V.E. Katsnelson's investigations on interrelations between left and right Blaschke-Potapov products.- 1. Some notation and preliminaries.- 2. On J-inner functions and their factorizations.- 3. On jpq-inner functions and generalized bitangential Schur-Nevanlinna-Pick interpolation.- 4. On V.E. Katsnelson's refinement of the factorization theory of J-inner functions.- 5. An inverse problem for A-singular jpq-inner functions.- References.- On some development of the S. Krein pencil theory.- References.- Discrete nonstationary bounded real lemma in indefinite metrics, the strict contractive case.- 1. Introduction.- 2. Preliminaries.- 3. Strict (J, J1) contractions: necessary conditions for a special case.- 4. Strict (J, J1) contractions: necessary conditions in the general case.- 5. The main results.- References.- Regularity of finite type critical points for self-adjoint operators in Krein space.- 1. Introduction and notation.- 2. Preliminary results.- 3. Regularity tests.- 4. ECR chains.- 5. General Krein spaces.- References.- Quasi-uniformly positive operators in Krein space.- 1. Quasi-uniformly positive operators.- 2. Quasi-uniformly positive forms.- 3. Klein-Gordon equation.- References.- Functional-differential and functional equations with rescaling.- 1. Introduction.- 2. Asymptotic behavior of the solutions.- 3. Compactly supported solutions. Wavelets and subdivision processes.- 4. Spectral methods in the theory of functional-differential equations, applications to quasi-crystals and localization theory.- 5. Probabilistic methods infunctional-differential equations theory.- 6. Invariant measures and chaos.- On the signatures of selfadjoint pencils.- 1. Introduction.- 2. The signatures of selfadjoint operators in Krein spaces.- 3. The Krein space environment.- 4. The Pontryagin space case.- 5. Applications to selfadjoint pencils.- References.- On the spectral theory of an elliptic boundary value problem involving an indefinite weight.- 1. Introduction.- 2. Preliminaries.- 3. Main results.- 4. Some technical results.- 5. Proof of theorem 3.4.- References.- Nonlinearity in H?-control theory, causality in the commutant lifting theorem, and extension of intertwining operators.- 0. Introduction.- 1. Systems.- 3. The linear optimization problem and the commutant lifting theorem.- 4. The nonlinear optimization problem and the iterative commutant lifting procedure.- 5. The causal LOP and the causal CLT.- 6. CLOP and CLT.- 7. Conclusion.- References.- Analysis of the radiation loss: asymptotics beyond all orders.- 1. Introduction.- 2. Asymptotic formulas.- 3. Radiation loss problems.- References.- Selfadjoint extensions of a closed linear relation of defect one in a Krein space.- 1. Selfadjoint closed linear relations with a finite number of negative squares...- 2. Nonnegative closed linear relations of defect one.- 3. Nonnegative closed linear relations of regular defect one.- 4. Nonnegative closed linear relations with a nonreal eigenvalue.- 5. The nonreal spectrum of the selfadjoint extensions.- 6. Selfadjoint extensions with an empty resolvent set.- 7. The resolvents of the selfadjoint extensions.- 8. The nonnegative selfadjoint extensions.- References.- Differential geometry of generalized Grassmann manifolds in C*-algebras.- 1. Environments and their Grassmannians.- 2. Topological properties.- 3.The standard lift.- 4. Differentiate structures.- 5. Invariant linear connections.- 6. Geodesics.- References.- Nonlinear equations and inverse spectral problems on the axis.- 1. On the Weyl-Titchmarsh matrix-function.- 2. Spectral data evolution.- 3. Investigation of the NSE and the MKdVE.- References.- Rayleigh problem and Friedrichs model.- 1. Introduction.- 2. Operator-theoretic formulation of the problem (2)-(3): generalized eigenfunctions.- 3. Spectral analysis of the problem (2)-(3): Friedrichs' model approach and expansion theorem.- 4. Scattering problem for Friedrichs' model related to the Rayleigh equation.- 5. Solvability class for inverse scattering problem. Local existence and uniqueness theorem.- References.- Yet another face of the creation operator.- References.- On transformations of canonical systems.- 0. Introduction.- 1. Some transformation rules.- 2. Changes of the spectral density by rational factors.- References.- Complementary triangular forms for infinite matrices.- 1. Introduction.- 2. Lower-upper factorization.- 3. Hilbert space analogues.- References.- List of participants.- List of lectures.