The spectrum of Schrödinger operators with positive potentials in Riemannian manifolds

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10 Scopus citations

Abstract

Let M be a noncompact complete Riemannian manifold. We consider the Schrödinger operator -Δ + V acting on L2(M), where V is a non-negative, locally integrable function on M. We obtain some simple conditions which imply that inf Spec(-Δ + V), the bottom of the spectrum of -Δ + V, is strictly positive. We also establish upper and lower bounds for the counting function N(λ).

Original languageEnglish
Pages (from-to)3447-3456
Number of pages10
JournalProceedings of the American Mathematical Society
Volume131
Issue number11
DOIs
StatePublished - Nov 2003

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics

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