Title

Self-adjoint extensions of differential operators on Riemannian manifolds

Document Type

Article

Publication Date

1-1-2016

Subject Area

ARRAY(0x5561e1ee0258)

Abstract

We study (Formula presented.), where D is a first order elliptic differential operator acting on sections of a Hermitian vector bundle over a Riemannian manifold M, and V is a Hermitian bundle endomorphism. In the case when M is geodesically complete, we establish the essential self-adjointness of positive integer powers of H. In the case when M is not necessarily geodesically complete, we give a sufficient condition for the essential self-adjointness of H, expressed in terms of the behavior of V relative to the Cauchy boundary of M.

Publication Title

Annals of Global Analysis and Geometry

Volume

49

Issue

1

First Page

87

Last Page

103

Digital Object Identifier (DOI)

10.1007/s10455-015-9482-0

ISSN

0232704X

E-ISSN

15729060

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