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At roughly 100 years of age operator theory remains a vibrant and exciting subject area with wide ranging applications. Many of the papers found here expand on lectures given at the 15th International Workshop on Operator Theory and Its Applications, held at the University of Newcastle upon Tyne from the 12th to the 16th of July 2004.
Contributions cover the main themes of the workshop: invariant subspaces, Krein space operator theory and its applications, multivariate operator theory and operator model theory, operator theory and function theory, systems theory including inverse scattering, structured matrices, and spectral theory of non-selfadjoint operators, including pseudodifferential and singular integral operators.
The book will appeal to both researchers and graduate students in mathematics, physics and engineering.
Inverse Scattering to Determine the Shape of a Vocal Tract.- Positivity and the Existence of Unitary Dilations of Commuting Contractions.- The Infinite-dimensional Continuous Time Kalman-Yakubovich-Popov Inequality.- From Toeplitz Eigenvalues through Green’s Kernels to Higher-order Wirtinger-Sobolev Inequalities.- The Method of Minimal Vectors Applied to Weighted Composition Operators.- The Continuous Analogue of the Resultant and Related Convolution Operators.- Split Algorithms for Centrosymmetric Toeplitz-plus-Hankel Matrices with Arbitrary Rank Profile.- Schmidt-Representation of Difference Quotient Operators.- Algebras of Singular Integral Operators with Piecewise Continuous Coefficients on Weighted Nakano Spaces.- Pseudodifferential Operators with Compound Slowly Oscillating Symbols.- Extension of Operator Lipschitz and Commutator Bounded Functions.- On the Kernel of Some One-dimensional Singular Integral Operators with Shift.- The Fredholm Property of Pseudodifferential Operators with Non-smooth Symbols on Modulation Spaces.- On Indefinite Cases of Operator Identities Which Arise in Interpolation Theory.- Singular Integral Operators in Weighted Spaces of Continuous Functions with Oscillating Continuity Moduli and Oscillating Weights.- Poly-Bergman Spaces and Two-dimensional Singular Integral Operators.- Weak Mixing Properties of Vector Sequences.