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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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An application of functional operator models to dissipative scattering theory
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by Daniel Alan Bondy PDF
Trans. Amer. Math. Soc. 223 (1976), 1-43 Request permission

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.
References
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Additional Information
  • © Copyright 1976 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 223 (1976), 1-43
  • MSC: Primary 47A40
  • DOI: https://doi.org/10.1090/S0002-9947-1976-0428077-9
  • MathSciNet review: 0428077