Schrödinger operators with locally integrable potentials on infinite metric graphs. Issue 12 (10th September 2017)

• Record Type: Journal Article
• Authors: Akduman, Setenay; Pankov, Alexander
• Is Part Of: Applicable analysis. Volume 96:Issue 12(2017)
• Page Start: 2149
• Page End: 2161
• Publication Date: 2017-09-10
• Subjects: Metric graph -- Schrödinger operator -- spectrum; 34B45 -- 34L40 -- 34B10 -- 81Q35; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2016.1207247
• Languages: English
• ISSNs: 0003-6811

Abstract

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.