On m-Accretivity of Perturbed Bochner Laplacian in L p Spaces on Riemannian Manifolds |
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Authors: | Ognjen Milatovic |
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Affiliation: | 1. Department of Mathematics and Statistics, University of North Florida, Jacksonville, FL, 32224, USA
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Abstract: | We consider a differential expression ${H=nabla^*nabla+V}We consider a differential expression H=?*?+V{H=nabla^*nabla+V}, where ?{nabla} is a Hermitian connection on a Hermitian vector bundle E over a manifold of bounded geometry (M, g) with metric g, and V is a locally integrable section of the bundle of endomorphisms of E. We give a sufficient condition for H to have an m-accretive realization in the space L p (E), where 1 < p < +∞. We study the same problem for the operator Δ M + V in L p (M), where 1 < p < ∞, Δ M is the scalar Laplacian on a complete Riemannian manifold M, and V is a locally integrable function on M. |
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