Lp positivity preservation and self-adjointness of Schrödinger operators on incomplete Riemannian manifolds

被引:0
|
作者
Bisterzo, Andrea [1 ]
Veronelli, Giona [2 ]
机构
[1] Sapienza Univ Roma, Rome, Italy
[2] Univ Milano Bicocca, Milan, Italy
关键词
Positivity preservation; essential self-adjointness; incomplete manifold; Schr & ouml; dinger operator; SCHRODINGER-OPERATORS; DIFFERENTIAL-OPERATORS;
D O I
10.1017/prm.2024.64
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
The aim of this paper is to prove a qualitative property, namely the preservation of positivity, for Schr & ouml;dinger-type operators acting on L-p functions defined on (possibly incomplete) Riemannian manifolds. A key assumption is a control of the behaviour of the potential of the operator near the Cauchy boundary of the manifolds. As a by-product, we establish the essential self-adjointness of such operators, as well as its generalization to the case p not equal 2, i.e. the fact that smooth compactly supported functions are an operator core for the Schr & ouml;dinger operator in L-p.
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页数:19
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