Self-adjoint extensions of differential operators on Riemannian manifolds

被引：0
作者：
Ognjen Milatovic
Françoise Truc
机构：
[1] University of North Florida,Department of Mathematics and Statistics
[2] Grenoble University,Unité mixte de recherche CNRS
来源：
Annals of Global Analysis and Geometry | 2016年 / 49卷
关键词：
Essential self-adjointness; Hermitian vector bundle; Higher-order differential operator; Riemannian manifold; Primary 58J50; 35P05; Secondary 47B25;
D O I：
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中图分类号：
学科分类号：
摘要：
We study H=D∗D+V\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H=D^*D+V$$\end{document}, 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.
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页码：87 / 103
页数：16
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