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Functional model for operators with spectrum on a curve
by
Alexey Tikhonov
Taurida National University, Ukraine
The functional model of S.-Nagy-Foias-Naboko is generalized for the case of operators with continuous spectrum on a smooth curve. We prove that trace class perturbations of normal operators with spectrum on a curve admit such model. Spectral components (absolutely continuous, singular, and other) are defined for this class of operators. Using the functional model as a tool we establish duality of spectral components for an operator and the adjoint operator to it. We apply obtained results to non-selfadjoint scattering theory and to extreme factorizations of J-contractive-valued functions (J-inner-outer, A-singular-regular).
Date received: May 29, 2002
Copyright © 2002 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caiz-32.