Limiting absorption principle, generalized eigenfunctions, and scattering matrix for Laplace operators with boundary conditions on hypersurfaces

  • Andrea Mantile

    Université de Reims Champagne-Ardenne, France
  • Andrea Posilicano

    Università dell’Insubria, Como, Italy
  • Mourad Sini

    Austrian Academy of Sciences, Linz, Austria
Limiting absorption principle, generalized eigenfunctions, and scattering matrix for Laplace operators with boundary conditions on hypersurfaces cover
Download PDF

A subscription is required to access this article.

Abstract

We provide a limiting absorption principle for the self-adjoint realizations of Laplace operators corresponding to boundary conditions on (relatively open parts of) compact hypersurfaces . For any of such self-adjoint operators we also provide the generalized eigenfunctions and the scattering matrix; both these objects are written in terms of operator-valued Weyl functions. We make use of a Krein-type formula which provides the resolvent difference between the operator corresponding to self-adjoint boundary conditions on the hypersurface and the free Laplacian on the whole space . Our results apply to all standard examples of boundary conditions, like Dirichlet, Neumann, Robin, and -type, either assigned on or on .

Cite this article

Andrea Mantile, Andrea Posilicano, Mourad Sini, Limiting absorption principle, generalized eigenfunctions, and scattering matrix for Laplace operators with boundary conditions on hypersurfaces. J. Spectr. Theory 8 (2018), no. 4, pp. 1443–1486

DOI 10.4171/JST/231