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Article overview
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On generalized Schr"odinger semigroups | Batu Güneysu
; | Date: |
1 Sep 2011 | Abstract: | We extend the Feynman-Kac formula for Schr"odinger type operators on vector
bundles over noncompact Riemannian manifolds to possibly very singular
potentials that appear in hydrogen like quantum mechanical problems and that
need not be bounded from below or locally square integrable. This path integral
formula is then used to prove several L^p-type results, like bounds on the
ground state energy and L^2 -> L^p smoothing properties of the corresponding
Schr"odinger semigroups. As another main result, we will prove that with a
little control on the Riemannian structure, the latter semigroups are also
L^2->{bounded continuous} smoothing for Kato decomposable potentials. These
results in particular apply to a very general class of magnetic Schr"odinger
operators on Riemannian manifolds. | Source: | arXiv, 1109.0151 | Services: | Forum | Review | PDF | Favorites |
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