Title

The m-accretivity of covariant Schrödinger operators with unbounded drift

Document Type

Article

Publication Date

6-1-2019

Subject Area

ARRAY(0x563cba3425b8)

Abstract

We work in the context of a geodesically complete Riemannian n-manifold M with a Hermitian vector bundle V over M, equipped with a metric covariant derivative ∇. We study the operator H: = ∇ †∇ + ∇ X+ V, where ∇ † is the formal adjoint of ∇ , the symbol ∇ X stands for the action of ∇ along a smooth vector field X on M, and V is a locally bounded section of the endomorphism bundle End V. We show that under certain conditions on X and V, the closure H|Cc∞(V)¯ of H|Cc∞(V) in Lp(V) , where 1 < p< ∞, is a maximal accretive operator. We also show that H|Cc∞(V)¯ coincides with the “maximal” realization of H in Lp(V).

Publication Title

Annals of Global Analysis and Geometry

Volume

55

Issue

4

First Page

657

Last Page

679

Digital Object Identifier (DOI)

10.1007/s10455-018-09645-6

ISSN

0232704X

E-ISSN

15729060

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