On m -accretive Schrödinger-type operators with singular potentials on manifolds of bounded geometry

Ognjen Milatovic

International Journal of Mathematics and Mathematical Sciences, 2003, vol. 2003, 1-9

Abstract:

We consider a Schrödinger-type differential expression ∇ ∗ ∇ + V , where ∇ is a C ∞ -bounded Hermitian connection on a Hermitian vector bundle E of bounded geometry over a manifold of bounded geometry ( M , g ) with positive C ∞ -bounded measure d μ , and V is a locally integrable linear bundle endomorphism. We define a realization of ∇ ∗ ∇ + V in L 2 ( E ) and give a sufficient condition for its m -accretiveness. The proof essentially follows the scheme of T. Kato, but it requires the use of a more general version of Kato's inequality for Bochner Laplacian operator as well as a result on the positivity of solution to a certain differential equation on M .

Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:176436

DOI: 10.1155/S0161171203209212

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