A GlazmanPovznerWienholtz Theorem on graphs
Abstract
The GlazmanPovznerWienholtz theorem states that the completeness of a manifold, when combined with the semiboundedness of the Schrödinger operator $\Delta + q$ and suitable local regularity assumptions on $q$, guarantees its essential selfadjointness. Our aim is to extend this result to Schrödinger operators on graphs. We first obtain the corresponding theorem for Schrödinger operators on metric graphs, allowing in particular distributional potentials $q\in H^{1}_{\rm loc}$. Moreover, we exploit recently discovered connections between Schrödinger operators on metric graphs and weighted graphs in order to prove a discrete version of the GlazmanPovznerWienholtz theorem.
 Publication:

arXiv eprints
 Pub Date:
 May 2021
 arXiv:
 arXiv:2105.09931
 Bibcode:
 2021arXiv210509931K
 Keywords:

 Mathematics  Spectral Theory;
 Mathematical Physics;
 Mathematics  Functional Analysis
 EPrint:
 24 pages