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The principle of limiting absorption for propagative systems in crystal optics with perturbations of long-range class

Published online by Cambridge University Press:  22 January 2016

Hideo Tamura
Hideo Tamura*
Affiliation:
Department of Engineering Mathematics Faculty of Engineering, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464, Japan
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The present paper is a continuation of [10] where we have proved the principle of limiting absorption for uniformly propagative systems with perturbations of long-range class. In this paper, we consider the Maxwell equation in crystal optics as an important example of non-uniformly propagative systems and, under the same assumptions on perturbations as in [10], we prove the principle of limiting absorption for the stationary problem associated with this equation by using a way similar to that in [10]. We here restrict our consideration to a very special class of non-uniformly propagative systems, but the method developed in this paper will be applicable to more general systems for which non-zero roots of characteristic equations of unperturbed systems are at most double. For another works on the spectral and scattering problems for non-uniformly propagative systems with perturbations of short-range class, see [1], [5], [6], [7] and [8], etc.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 84 , December 1981 , pp. 169 - 193
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1981

References

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