This volume brings readers up to date on different aspects of operator theory and its applications, including mathematical physics, hydrodynamics, magnetohydrodynamics, quantum mechanics, astrophysics as well as the theory of networks and systems. Of practical use to a wide readership in pure and applied mathematics, physics and engineering sciences.
Inversion formulas for compressions of block-Toeplitz operators.- 1. Introduction.- 2. Main results.- 3. Inversion formulas for block-Toeplitz and block-Pick matrices.- 4. Inversion formulas for block-Toeplitz integral operators in 5-1 (0, a) (a < ?).- References.- Contractive linear relations in Pontryagin spaces.- 1. Introduction.- 2. Contractive linear relations.- 3. Regularization.- 4. Criteria for maximality.- 5. Properties of maximal contractive linear relations.- 6. Invariant subspaces.- References.- On a new algorithm for almost periodic factorization.- 1. Introduction.- 2. Known results.- 3. The reduction procedure.- 4. Matrices with regular Fourier spectra.- 5. Repeated use of the reduction procedure.- 6. Trinomial f.- 7. Block matrix generalizations.- 8. Final remarks.- References.- On the normal solvability of cohomological equations on compact topological spaces.- 1. Introduction.- 2. Dynamical lemmas.- 3. Proof of the Main Theorem.- 4. Appendix.- References.- On nonnegative realizations of rational matrix functions and nonnegative input-output systems.- 1. Introduction.- 2. Nonnegative realizations of rational matrix functions.- 3. Nonnegative input output systems.- 4. Appendix.- References.- On the geometric structure of regular dilations.- 1. Notations and preliminaries.- 2. The structure of regular and *-regular isometric dilations.- 3. Functional model and maximal function for a bicontraction having a *-regular dilation.- References.- On generalized interpolation and shift invariant maximal semidefinite subspaces.- 1. Introduction.- 2. Preliminaries.- 3. Generalized interpolation.- 4. The bitangential Nevanlinna-Pick problem.- References.- The sum of matrix Nevanlinna functions and self-adjoint extensions in exit spaces.- 1. Introduction.- 2. Nevanlinna pairs.- 3. Kre 6-1 n’s formula.- 4. The sum of Q-functions.- 5. The orthogonal sum of Sturm-Liouville operators.- 6. Schur complements of Q-functions.- 7. Nevanlinna functions and exit spaces.- References.- Properties of “derived” Hankel matrices.- 1. Introduction.- 2. Representations of m-derived Hankel matrices.- 3. Vandermonde factorization.- 4. Generating functions and Bezoutians.- 5. Triangular derived Hankel matrices.- References.- The probability that a (partial) matrix is positive semidefinite.- 1. Introduction.- 2. The case of full matrices.- 3. The case of partial matrices.- 4. The probability of the existence of a positive semidefinite completion.- References.- Factorization of lower triangular unitary operators with finite Kronecker index into elementary factors.- 1. Introduction.- 2. Unitary time varying systems.- 3. Observability and controllability of unitary time varying systems.- 4. A realization theorem.- 5. Cascade connection and factorization.- 6. Proof of Theorems 1.1 and 1.2.- 7. Main theorems for operators in the class LK.- References.- Fredholm theory of interpolation morphisms.- 1. Introduction.- 2. Fredholm theory in a paraalgebra of interpolation morphisms.- 3. Interpolation of Fredholm elements.- 4. Perturbation results for the real interpolation methods.- References.- Resolvents of symmetric operators and the degenerated Nevanlinna-Pick problem.- 1. Introduction.- 2. Straus extensions.- 3. The u-resolvents of S.- 4. The degenerated Nevanlinna-Pick problem.- 5. Explicit formulas.- References.- Perturbation of linear semigroups.- 1. Introduction.- 2. Essential spectral radius for perturbed semigroups.- References.- On the approximation of operators and the convergence of the spectra of the approximants.- 1. Introduction.- 2. The main result.- 3. Auxiliary results and proofs.- References.
