Nelia Charalambous, Zhiqin Lu
Abstract
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In this article we prove a generalization of Weyl's criterion for the essential spectrum of a self-adjoint operator on a Hilbert space. We then apply this criterion to the Laplacian on functions over open manifolds and get new results for its essential spectrum.
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In this article we prove a generalization of Weyl's criterion for the essential spectrum of a self-adjoint operator on a Hilbert space. We then apply this criterion to the Laplacian on functions over open manifolds and get new results for its essential spectrum.
Key concepts: Essential spectrum, Generalization, Spectrum (functional analysis), Laplace operator, Hilbert space, Mathematics, Pure mathematics, Operator (biology)