Schrödinger operators on graphs and geometry I: Essentially bounded potentials

Research output: Contribution to journalArticle

Abstract

The inverse spectral problem for Schrödinger operators on finite compact metric graphs is investigated. The relations between the spectral asymptotics and geometric properties of the underlying graph are studied. It is proven that the Euler characteristic of the graph can be calculated from the spectrum of the Schrödinger operator in the case of essentially bounded real potentials and standard boundary conditions at the vertices. Several generalizations of the presented results are discussed.

Details

Authors
  • Pavel Kurasov
Organisations
Research areas and keywords

Subject classification (UKÄ) – MANDATORY

  • Mathematics

Keywords

  • Quantum, graph, Trace formula, Euler characteristic
Original languageEnglish
Pages (from-to)934-953
JournalJournal of Functional Analysis
Volume254
Issue number4
Publication statusPublished - 2008
Publication categoryResearch
Peer-reviewedYes