International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 2003 / Article

Open Access

Volume 2003 |Article ID 176436 | https://doi.org/10.1155/S0161171203209212

Ognjen Milatovic, "On m-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 m-accretive Schrödinger-type operators with singular potentials on manifolds of bounded geometry

Received20 Sep 2002

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 dμ, and V is a locally integrable linear bundle endomorphism. We define a realization of +V in L2(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.

Copyright © 2003 Hindawi Publishing Corporation. 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.


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