THE SPECTRUM OF k-FORM SCHRÖDINGER LAPLACIANS ON CONFORMALLY CUSP MANIFOLDS
نویسنده
چکیده
We describe the spectrum of the k-form Laplacian on conformally cusp Riemannian manifolds. The essential spectrum is shown to vanish precisely when the k and k − 1 de Rham cohomology groups of the boundary vanish. We give Weyl-type asymptotics for the eigenvalue-counting function in the purely discrete case. In the other case we analyze the essential spectrum via positive commutator methods. We also exhibit a class of potentials V such that the Schrödinger operator has compact resolvent, although V tends to −∞ in most of the infinity.
منابع مشابه
The Spectrum of Schrödinger Operators and Hodge Laplacians on Conformally Cusp Manifolds
We describe the spectrum of the k-form Laplacian on conformally cusp Riemannian manifolds. The essential spectrum is shown to vanish precisely when the k and k − 1 de Rham cohomology groups of the boundary vanish. We give Weyl-type asymptotics for the eigenvalue-counting function in the purely discrete case. In the other case we analyze the essential spectrum via positive commutator methods and...
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تاریخ انتشار 2008