Singular Schrödinger operators with prescribed spectral properties

This paper deals with singular Schrödinger operators of the form−d2dx2+∑k∈Zγkδ(⋅−zk),γk∈R, in L2(ℓ−,ℓ+), where δ(⋅−zk) is Dirac delta-function supported at zk∈(ℓ−,ℓ+) and (ℓ−,ℓ+) a bounded interval. It will be shown that interaction strengths γk points zk can chosen such way essential spectrum part discrete this self-adjoint operator coincide prescribed sets on real line.