On the spectrum of the reduced wave operator with cylindrical discontinuity

Details On the spectrum of the reduced wave operator with cylindrical discontinuity On the spectrum of the reduced wave operator with cylindrical discontinuity

1999-02-14

arxiv.org/abs/math/9902085v1

Forum Mathematicum 9 (1997) 29-60

Mathematics

Spectral Theory

36 pages; no figures

Scientific paper

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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