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On the spectrum of the reduced wave operator with cylindrical discontinuity

On the spectrum of the reduced wave operator with cylindrical discontinuity Abstract. Consider the differential operator //= -- () 1 in the Hubert space X = L2(RN', ()), where is the Laplacian in RN, and () is a positive simple function on RN. Let S be the surface on which is discontinuous (the separating surface). So far the stratified media in which the separating surface S consists of parallel surfaces 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 priori estimates of radiation condition term. 1991 Mathematics Subject Classification: 35P05. §1. Introduction Consider the differential expression (1.1) = -()- 1 . Here is the Laplacian in RN with N > 2, and () is a positive function on RN given by (1.2) (*) where 1( 2 > , 2, and ,, 7 = 1,2, are open sets of RN such that This work was supported by Deutsche Forschungsgemeinschaft through SFB 359. W. J ger, . Saito | being the closure of {. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Forum Mathematicum de Gruyter

On the spectrum of the reduced wave operator with cylindrical discontinuity

Forum Mathematicum , Volume 9 (9) – Jan 1, 1997

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References (17)

Publisher
de Gruyter
Copyright
Copyright © 2009 Walter de Gruyter
ISSN
0933-7741
eISSN
1435-5337
DOI
10.1515/form.1997.9.29
Publisher site
See Article on Publisher Site

Abstract

Abstract. Consider the differential operator //= -- () 1 in the Hubert space X = L2(RN', ()), where is the Laplacian in RN, and () is a positive simple function on RN. Let S be the surface on which is discontinuous (the separating surface). So far the stratified media in which the separating surface S consists of parallel surfaces 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 priori estimates of radiation condition term. 1991 Mathematics Subject Classification: 35P05. §1. Introduction Consider the differential expression (1.1) = -()- 1 . Here is the Laplacian in RN with N > 2, and () is a positive function on RN given by (1.2) (*) where 1( 2 > , 2, and ,, 7 = 1,2, are open sets of RN such that This work was supported by Deutsche Forschungsgemeinschaft through SFB 359. W. J ger, . Saito | being the closure of {.

Journal

Forum Mathematicumde Gruyter

Published: Jan 1, 1997

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