On the Spectrum of the Reduced Wave Operator with Cylindrical Discontinuity

Academic Article


  • Consider the differential operator H= - μ(x)-1Δ in the Hubert space X = L2(RN; i(x)dx), where Δ is the Laplacian in RN, and μ(x) 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. © 1997, Walter de Gruyter. All rights reserved.
  • Authors

    Published In

  • Forum Mathematicum  Journal
  • Digital Object Identifier (doi)

    Pubmed Id

  • 16552287
  • Author List

  • Jäger W; Saitō Y
  • Start Page

  • 29
  • End Page

  • 60
  • Volume

  • 9
  • Issue

  • 9