Singular Schrödinger operators with prescribed spectral properties

Jussi Behrndt*, Andrii Khrabustovskyi

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


This paper deals with singular Schrödinger operators of the form −[Formula presented]+∑k∈Zγkδ(⋅−zk),γk∈R, in L2(ℓ,ℓ+), where δ(⋅−zk) is the Dirac delta-function supported at zk∈(ℓ,ℓ+) and (ℓ,ℓ+) is a bounded interval. It will be shown that the interaction strengths γk and the points zk can be chosen in such a way that the essential spectrum and a bounded part of the discrete spectrum of this self-adjoint operator coincide with prescribed sets on the real line.

Original languageEnglish
Article number109252
JournalJournal of Functional Analysis
Issue number1
Publication statusPublished - 1 Jan 2022


  • Discrete spectrum
  • Essential spectrum
  • Schrödinger operator
  • δ-Interaction

ASJC Scopus subject areas

  • Analysis


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