This volume contains a selection of papers on modern operator theory and its applications, arising from a joint workshop on linear one-dimensional singular integral equations. The book is of interest to a wide audience in the mathematical and engineering sciences.
Inverse scattering problem for differential operators with rational scattering matrix functions.- 1. Introduction.- 2. Rational matrix valued functions.- 3. Minimal realizations of rational scattering functions.- 4. Marchenko’s equation in the rational case.- 5. Formula for the potential.- 6. Equivalence with Krein’s approach.- 7. A result on asymptotic expansions.- 8. Reconstructing the potential.- References.- Banach algebras generated by N idempotents and applications.- Preface and acknowledgement.- 1. Introduction.- 2. Algebras generated by two idempotents.- 3. Algebras generated by three idempotents.- 4. An N projections theorem.- 5. Examples.- 6. Miscellanea.- References.- Toeplitz operators with discontinuous symbols: Phenomena beyond piecewise continuity.- 1. Introduction.- 2. Preliminaries.- 3. Periodic and u-periodic symbols.- 4. Orientation preserving whirls.- 5. Concrete orientation preserving whirls.- 6. Orientation changing whirls.- 7. Undecided symbols with bounded arguments.- 8. Modulated almost periodic symbols.- References.- Toeplitz and singular integral operators on general Carleson Jordan curves.- 1. Introduction.- 2. The first three metamorphoses.- 3. Main result.- 4. Examples.- 5. Plan of the proof of the main theorem.- 6. Submultiplicative functions.- 7. Description of the set Nt.- 8. Description of the set ?t.- 9. Spectra and essential spectra of Toeplitz operators.- 10.The algebra of singular integral operators.- References.- Weighted uniform convergence of the quadrature method for Cauchy singular integral equations.- 1. Introduction.- 2. Notations and preliminary results.- 3. The quadrature method.- 4. Special interpolation processes.- 5. Numerical examples.- References.- Symbol calculus for singular integrals with operator-valued PQC-coefficients.- 1. Introduction.- 2. Operator-valued quasicontinuous functions.- 3. Symbol calculus.- References.- Finite section method for singular integrals with operator-valued PQC-coefficients.- 1. Introduction.- 2. Preliminaries.- 3. A generalization of compactness and of strong convergence.- 4. Algebraization of stability and lifting theorem.- 5. The algebras S(PQCL(H)) and F(PQCL(H)).- 6. Localization.- 7. Identification of local algebras.- 8. The algebras ? and ?.- 9. Identification of local algebras continued.- 10.Final result.- References.- Distribution of zeros of orthogonal functions related to the Nehari problem.- 1. Introduction.- 2. Auxilliary theorems.- 3. Proof of the main theorem.- References.- Semi-Fredholm properties of certain singular integral operators.- 1. Introduction.- 2. Operators with almost periodic symbols.- 3. Operators with semi almost periodic symbols.- References.- On canonical factorization of dissipative and positive matrix functions relative to non-simple contours.- References.- Asymptotic invertibility of Toeplitz operators.- 1. Introduction.- 2. Operators.- 3. Finite sections and algebras.- 4. Symbols.- 5. Pseudospectra.- 6. Asymptotic Moore-Penrose invertibility.- References.- Calculation of the norm of polynomials of two adjoint projections.- 0. Introduction.- 1. Some necessary results.- 2. The main results.- 3. Additional remarks and examples.- References.- Toeplitz Lectures 1995.- Lectures of the Joint German-Israeli Workshop.
