Integral Equations and Operator Theory

, Volume 2, Issue 1, pp 69–115 | Cite as

Spectral analysis for perturbed Laplace operators in cylindrical domains

  • Hideo Tamura
Article

Abstract

The spectral theory for perturbed Laplace operators which are defined over cylindrical domains with bounded cross-sections is studied. The perturbation to be discussed here belongs to the so-called long-range class. First the following problems are considered: (i) discreteness of eigenvalues, (ii) absolute continuity of continuous spectrum, (iii) limiting absorption principle. Secondly the asymptotic behavior of solutions obtained by the limiting absorption method at infinity is discussed. These are generalizations of the results which have been obtained by many authors in the case of the short-range perturbation. Especially, the result concerning the asymptotic behavior includes a new one.

Keywords

Asymptotic Behavior Spectral Analysis Laplace Operator Continuous Spectrum Spectral Theory 

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Copyright information

© Birkhäuser Verlag 1979

Authors and Affiliations

  • Hideo Tamura
    • 1
  1. 1.Department of Engineering Mathematics Faculty of EngineeringNagoya UniversityNagoyaJapan

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