Title | Recent Developments in Operator Theory and Its Applications [electronic resource] : International Conference in Winnipeg, October 2-6, 1994 / edited by I. Gohberg, P. Lancaster, P. N. Shivakumar |
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Imprint | Basel : Birkhรคuser Basel, 1996 |
Connect to | http://dx.doi.org/10.1007/978-3-0348-9035-9 |
Descript | XII, 436 p. online resource |
Inverse scattering problem for continuous transmission lines with rational reflection coefficient function -- 1. Introduction -- 2. Some results on differential expressions -- 3. The reflection coefficient function -- 4. The rational case -- References -- The band method and the Grassmannian approach for completion and extension problems -- 1. Introduction -- 2. The Grassmannian approach -- 3. Proofs of theorems 2.2 and 2.3 -- 4. The Caratheodory and Nehari extension problems -- 5. Operator matrix extension problems -- References -- Polar decompositions in finite dimensional indefinite scalar product spaces: Special cases and applications -- 1. Introduction -- 2. H-contractive matrices -- 3. H-plus matrices -- 4. Indefinite scalar products with only one positive square -- 5. Polar decompositions with special unitary factors -- 6. Applications: Linear optics -- References -- Positive differential operators in Krein space L2(R) -- 1. Abstract results -- 2. Differential operators with constant coefficients -- 3. Half-range completeness -- References -- Elliptic problems involving an indefinite weight function -- 1. Introduction -- 2. Preliminaries -- 3. Main results -- 4. Examples -- References -- The KDV hierarchy and associated trace formulas -- 1. Introduction -- 2. The KDV hierarchy, recursion relations, and hyperelliptic curves -- 3. The stationary formalism -- 4. The time-dependent formalism -- 5. General trace formulas -- Appendix A. Hyperelliptic curves of the KDV-type and theta functions -- Appendix B. An explicit illustration of the Riemann-Roch theorem -- References -- On spectral properties of Schrรถdinger-type operator with complex potential -- 1. General perturbation results -- 2. Application to the Schrodinger-type operator -- Appendix 1. Proof of Theorem 1 -- Appendix 2. Proof of Theorem 6 -- Appendix 3. The subordination condition -- References -- Coalgebras and spectral theory in one and several parameters -- 1. Introduction -- 2. Coalgebras and comodules -- 3. The coalgebra dual of a polynomial algebra -- 4. The primary decomposition theorem -- 5. Monic matrix polynomials -- 6. Several commuting maps -- 7. Multiparameter systems -- References -- Destabilization of infinite-dimensional time-varying systems via dynamical output feedback -- 1. Introduction -- 2. Notation and fundamental results -- 3. System description -- 4. Problem formulation -- 5. Destabilization results -- References -- Perturbations of G-selfadjoint operators and operator polynomials with real spectrum -- 1. Introduction -- 2. Perturbations of finite rank -- 3. Small and compact perturbations -- 4. Applications to operator polynomials -- 5. A factorization theorem in the monic case -- 6. Differential equations with stably bounded solutions -- 7. The case of noninvertible leading coefficient -- References -- Definitizable G-unitary operators and their applications to operator polynomials -- 1. Introduction -- 2. Preliminary definitions and results -- 3. Compact perturbations -- 4. Operator polynomials quasihyperbolic on T -- 5. Other charcterizations of QHP on T -- References -- System theoretic aspects of completely symmetric systems -- 1. Introduction -- 2. Discrete time systems -- 3. Continuous-time systems -- References -- Contractive completion of block matrices and its application to H? control of periodic systems -- 1. Introduction -- 2. H? periodic control and lifting -- 3. Matrix contractive completion -- 4. All H? suboptimal periodic controllers -- 5. Concluding remarks -- Appendix: Proof of Theorem 1 -- References -- Spline approximation methods for Wiener-Hopf operators -- 1. Introduction -- 2. Technical preliminaries -- 3. An algebra of approximation sequences for Wiener-Hopf operators -- 4. Approximation methods for composed operators -- References -- Inertia conditions for the minimization of quadratic forms in indefinite metric spaces -- 1. Introduction -- 2. An inertia result for linear transformations -- 3. The indefinite-weighted least-squares problem -- 4. The equivalent estimation problem -- 5. Relations between the IWLS and EE problems -- 6. Incorporating state-space structure -- 7. A recursive IWLS problem in the presence of state-space structure -- 8. An application to H?-filtering -- 9. An application to robust adaptive filters -- 10. An application to total least-squares methods -- 11. Concluding remarks -- References -- Bounds for the width of the instability intervals in the Mathieu equation -- 1. Introduction -- 2. Preliminaries -- References -- Operator pencils arising in elasticity and hydrodynamics: The instability index formula -- 1. Classes of unbounded operator pencils -- 2. Root subspaces of linear dissipative pencils and their properties -- 3. Quadratic dissipative pencils and the instability index formula -- 4. Applications -- References -- Toeplitz-like operators and their finite sections -- 1. Introduction -- 2. The main results -- 3. Proofs -- References -- Spectral representations and spectral functions of symmetric operators -- 0. Introduction -- 1. Spectral representations of linear operators -- 2. Selfadjoint extension in a larger Hilbert space -- 3. The generalized spectral function of a symmetric operator and the corresponding spectral transformation -- 4. Generalized resolvents of a symmetric operator -- References -- Hankel type operators, Bourgain algebras, and isometries -- 1. Hankel type operators and Bourgain algebras -- 2. Complete continuity of Hankel type operators and isometries -- 3. Biholomorphic equivalence and Bourgain algebras -- References -- Effective computation of operators defined by line integrals -- 1. Introduction -- 2. Numerical procedure -- 3. Modified Gaussian quadratures -- 4. Piecewise modified Guassian quadrature on an interval -- 5. The calculation of line integrals -- 6. Extension for the calculation of operators defined by Cauchy principal value integrals -- References