Schrödinger operators with locally integrable potentials on infinite metric graphs

Abstract

The paper is devoted to Schrödinger operators on infinite metric graphs. We suppose that the potential is locally integrable and its negative part is bounded in certain integral sense. First, we obtain a description of the bottom of the essential spectrum. Then we prove theorems on the discreteness of the negative part of the spectrum and of the whole spectrum that extend some classical results for one dimensional Schrödinger operators.

Keywords:

• Metric graph
• Schrödinger operator
• spectrum

AMS Subject Classifications:

• 34B45
• 34L40
• 34B10
• 81Q35

Notes

No potential conflict of interest was reported by the authors.