Ognjen Milatovic, "On -accretive Schrödinger-type operators with singular potentials on manifolds of bounded geometry", International Journal of Mathematics and Mathematical Sciences, vol. 2003, Article ID 176436, 9 pages, 2003. https://doi.org/10.1155/S0161171203209212
On -accretive Schrödinger-type operators with singular potentials on manifolds of bounded geometry
We consider a Schrödinger-type differential expression , where is a -bounded Hermitian connection on a Hermitian vector bundle of bounded geometry over a manifold of bounded geometry with positive -bounded measure , and is a locally integrable linear bundle endomorphism. We define a realization of in and give a sufficient condition for its -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 .
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