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ON $m$-ACCRETIVE SCHRÖDINGER OPERATORS IN $L^1$-SPACES ON MANIFOLDS OF BOUNDED GEOMETRY

Published online by Cambridge University Press:  04 February 2008

Ognjen Milatovic
Ognjen Milatovic
Affiliation:
Department of Mathematics and Statistics, University of North Florida, Jacksonville, FL 32224, USA (omilatov@unf.edu)
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Abstract

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Let $(M,g)$ be a manifold of bounded geometry with metric $g$. We consider a Schrödinger-type differential expression $H=\Delta_M+V$, where $\Delta_M$ is the scalar Laplacian on $M$ and $V$ is a non-negative locally integrable function on $M$. We give a sufficient condition for $H$ to have an $m$-accretive realization in the space $L^1(M)$.špace{-4pt}

Keywords

Primary 58J5035P05bounded geometry$L^1$-space$m$-accretivemanifoldSchrödinger operator}špace{-2pt
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 51 , Issue 1 , February 2008 , pp. 215 - 227
Copyright
Copyright © Edinburgh Mathematical Society 2008