TY - JOUR
T1 - Singular Schrödinger operators with prescribed spectral properties
AU - Behrndt, Jussi
AU - Khrabustovskyi, Andrii
N1 - Funding Information:
This research was started when A.K. was a postdoctoral researcher at Graz University of Technology; he gratefully acknowledges financial support of the Austrian Science Fund (FWF) through the project M 2310-N32 . The work of A.K. is also partly supported by the Czech Science Foundation (GAČR) through the project 21-07129S . J.B. gratefully acknowledges financial support by the Austrian Science Fund (FWF): P 33568-N . This publication is based upon work from COST Action CA 18232 MAT-DYN-NET, supported by COST ( European Cooperation in Science and Technology ), www.cost.eu .
Publisher Copyright:
© 2021 The Authors
PY - 2022/1/1
Y1 - 2022/1/1
N2 - 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.
AB - 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.
KW - Discrete spectrum
KW - Essential spectrum
KW - Schrödinger operator
KW - δ-Interaction
UR - http://www.scopus.com/inward/record.url?scp=85117167481&partnerID=8YFLogxK
U2 - 10.1016/j.jfa.2021.109252
DO - 10.1016/j.jfa.2021.109252
M3 - Article
AN - SCOPUS:85117167481
SN - 0022-1236
VL - 282
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
IS - 1
M1 - 109252
ER -