Electron. J. Diff. Eqns.,
Vol. 2003(2003), No. 64, pp. 18.
Selfadjointness of Schrodingertype operators
with singular potentials on manifolds of bounded geometry
Ognjen Milatovic
Abstract:
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
selfadjoint bundle endomorphisms. We give a sufficient condition
for selfadjointness 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, selfadjointness, manifold,
bounded geometry, singular potential
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Ognjen Milatovic
78 Apsley Street, Apt. 1
Hudson, MA 01749, USA
email: omilatov@unf.edu

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