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On the spectrum of the reduced wave operator with cylindrical discontinuity | | Willi Jager
; Yoshimi Saito
; | | Date: |
14 Feb 1999 | | Journal: | Forum Mathematicum 9 (1997) 29-60 | | Subject: | Spectral Theory | math.SP | | 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. | | Source: | arXiv, math.SP/9902085 | | Services: | Forum | Review | PDF | Favorites | |
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