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

Ognjen Milatovic — 2004

Commentationes Mathematicae Universitatis Carolinae

We consider a Schrödinger-type differential expression H V = ∇ * ∇ + 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 metric g and positive C ∞ -bounded measure d μ , and V is a locally integrable section of the bundle of endomorphisms of E . We give a sufficient condition for m -sectoriality of a realization of H V in L 2 ( E ) . In the proof we use generalized Kato’s inequality as well as a result on the positivity of u ∈ L 2 ( M ) satisfying the...

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