Operator Theory and Boundary Eigenvalue Problems de I. Gohberg

Operator Theory and Boundary Eigenvalue Problems: International Workshop in Vienna, July 27–30, 1993: Operator Theory: Advances and Applications, cartea 80

I. Gohberg

H. Langer

The Workshop on Operator Theory and Boundary Eigenvalue Problems was held at the Technical University, Vienna, Austria, July 27 to 30, 1993. It was the seventh workshop in the series of IWOTA (International Workshops on Operator Theory and Applications). The main topics at the workshop were interpolation problems and analytic matrix functions, operator theory in spaces with indefinite scalar products, boundary value problems for differential and functional-differential equations and systems theory and control. The workshop covered different aspects, starting with abstract operator theory up to contrete applications. The papers in these proceedings provide an accurate cross section of the lectures presented at the workshop. This book will be of interest to a wide group of pure and applied mathematicians.

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Cuprins

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.