Essential self-adjointness and the $L^2$-Liouville property

Bobo Hua; Jun Masamune; Radosław K. Wojciechowski

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arXiv · 2012.08936

Essential self-adjointness and the $L^2$-Liouville property

Bobo Hua·Jun Masamune·Radosław K. Wojciechowski

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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.

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BibTeX RIS

Bobo Hua, Jun Masamune, Radosław K. Wojciechowski. 2020-12-01. Essential self-adjointness and the $L^2$-Liouville property. https://arxiv.org/abs/2012.08936

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