On the spectrum of the reduced wave operator with cylindrical discontinuity

Willi Jager; Yoshimi Saito

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arXiv · math/9902085

On the spectrum of the reduced wave operator with cylindrical discontinuity

Willi Jager·Yoshimi Saito

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Abstract

Consider the differential operator H = -(1/m(x))L, where L is the N-dimensional Laplacian, in the weighted Hilbert space of square integrable functions on N-dimensional Euclidean space with weight m(x)dx. Here m(x) is a positive step function with a surface S of discontinuity (the separation surface). So far the stratified media in which the separating surface S consists of paralell planes have been vigorously studied. Also the case where S has a cone shape has been discussed. In this work we shall deal with a new type of discontinuity which we call cylindrical discontinuity. Under this condition we shall use the limiting absorption method to prove that H is absolute continuous. Our method is based on a apriori estimates of radiation condition term.

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BibTeX RIS

Willi Jager, Yoshimi Saito. 1999-02-14. On the spectrum of the reduced wave operator with cylindrical discontinuity. https://arxiv.org/abs/math/9902085

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