Essential self-adjointness for combinatorial Schrödinger operators II- Metrically non complete graphs

Abstract

We consider weighted graphs, we equip them with a metric structure given by a weighted distance, and we discuss essential self-adjointness for weighted graph Laplacians and Schrödinger operators in the metrically non complete case.

Revisited version: Ognjen Milatovic wrote to us that he had discovered a gap in the proof of theorem 4.2 of our paper. As a consequence we propose to make an additional assumption (regularity property of the graph) to this theorem. A new subsection (4.1) is devoted to the study of this property and some details have been changed in the proof of theorem 4.2

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Cited by in corpus (7)

• Dirac and magnetic Schrödinger operators on fractals
• The problem of deficiency indices for discrete Schrödinger operators on locally finite graphs
• Essential self-adjointness of magnetic Schrödinger operators on locally finite graphs
• Spectral Theory of Infinite Quantum Graphs
• Self-adjoint and Markovian extensions of infinite quantum graphs
• Spectral and scattering theory for Gauss-Bonnet operators on perturbed topological crystals
• A Glazman-Povzner-Wienholtz Theorem on graphs