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Resonances and resonance expansions for point interactions on the half-space
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Resonances and resonance expansions for point interactions on the half-space
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Paper
Resonances and resonance expansions for point interactions on the half-space
2024
Overview
In this paper we describe the resonances of the singular perturbation of the Laplacian on the half space \\(\\Omega =\\mathbb R^3_+\\) given by the self-adjoint operator named \\(\\delta\\)-interaction or point interaction. We will assume Dirichlet or Neumann boundary conditions on \\(\\partial \\Omega\\). At variance with the well known case of \\(\\mathbb R^3\\), the resonances constitute an infinite set, here completely characterized. Moreover, we prove that resonances have an asymptotic distribution satisfying a modified Weyl law. Finally we give applications of the results to the asymptotic behavior of the abstract Wave and Schr\"odinger dynamics generated by the Laplacian with a point interaction on the half-space.
Publisher
Cornell University Library, arXiv.org
