International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 38, Pages 2415-2423
On -accretive Schrödinger-type operators with singular potentials on manifolds of bounded geometry
Department of Mathematics, Fitchburg State College, 160 Pearl Street, Fitchburg 01420, MA, USA
Received 20 September 2002
Copyright © 2003 Ognjen Milatovic. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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 .