The spectral bound of Schrodinger operators

Journal article

Let V : RN → [0, ∞] be a measurable function, and λ > 0 be a parameter. We consider the behaviour of the spectral bound of the operator 1/2Δ - λV as a function of λ. In particular, we give a formula for the limiting value as λ → ∞, in terms of the integrals of V over subsets of RN on which the Laplacian with Dirichlet boundary conditions has prescribed values. We also consider the question whether this limiting value is attained for finite λ. © 1996 Kluwer Academic Publishers.

Authors: Arendt, W; Batty, C

• Publication status: Published
• Journal: POTENTIAL ANALYSIS
• Volume: 5
• Issue: 3
• Pages: 207-230
• Publication date: 1996-06-01
• ISSN: 0926-2601
• Keywords: Schrodinger semigroup; spectral bound; spectral function