Essential self-adjointness and the $L^2$-Liouville property
Spectral Theory
2021-02-18 v2 Mathematical Physics
math.MP
Abstract
We discuss connections between the essential self-adjointness of a symmetric operator and the constancy of functions which are in the kernel of the adjoint of the operator. We then illustrate this relationship in the case of Laplacians on both manifolds and graphs. Furthermore, we discuss the Green's function and when it gives a non-constant harmonic function which is square integrable.
Keywords
Cite
@article{arxiv.2012.08936,
title = {Essential self-adjointness and the $L^2$-Liouville property},
author = {Bobo Hua and Jun Masamune and Radosław K. Wojciechowski},
journal= {arXiv preprint arXiv:2012.08936},
year = {2021}
}