We consider the Schrodinger type differential expression
where is a -bounded Hermitian connection on a Hermitian vector bundle of bounded geometry over a manifold of bounded geometry with metric and positive -bounded measure , and , where in and in are linear self-adjoint bundle endomorphisms. We give a sufficient condition for self-adjointness of the operator in defined by for all . The proof follows the scheme of Kato, but it requires the use of more general version of Kato's inequality for Bochner Laplacian operator as well as a result on the positivity of satisfying the equation , where is the scalar Laplacian on , is a constant and is a positive distribution on .
Submitted May 13, 2003. Published June 11, 2003.
Math Subject Classifications: 35P05, 58J50, 47B25, 81Q10.
Key Words: Schrodinger operator, self-adjointness, manifold, bounded geometry, singular potential
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|Ognjen Milatovic |
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