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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



An application of functional operator models to dissipative scattering theory

Author: Daniel Alan Bondy
Journal: Trans. Amer. Math. Soc. 223 (1976), 1-43
MSC: Primary 47A40
MathSciNet review: 0428077
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Abstract: An abstract framework for dissipative scattering theory is developed and then applied to two systems previously considered by P. Lax and R. S. Phillips. Results relating the poles and zeroes of the scattering matrix to the spectra of the infinitesimal generators A (which generates the semigroup formed by mapping initial data into solution data at time t) and B (which generates a “local” semigroup) are proven. In particular these results are shown to follow from the fact that the characteristic function of A (appropriately defined) and the scattering matrix combine to form the characteristic function of B.

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Keywords: Characteristic functions, dissipative scattering theory
Article copyright: © Copyright 1976 American Mathematical Society