Essential self-adjointness and the L²-Liouville property

2020/12/01 by Bobo Hua, Hua, Bobo, Jun Masamune +3 · 2 citations
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical methods in inverse problems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2012.08936

openalex publication_date 2020/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• Essential self-adjointness of non-semibounded Schrödinger operators on infinite graphs
• Form uniqueness for graphs with weakly spherically symmetric ends

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