Singular Schrodinger operators with prescribed spectral properties

Abstract

This paper deals with singular Schrodinger operators of the form -d(2)/dx(2) + Sigma(k is an element of Z) gamma(k)delta(. - z(k)), gamma(k) is an element of R, in L-2 (l(-), l(+)), where delta(. - z(k)) is the Dirac delta-function supported at z(k) is an element of (l(-), l(+)) and (l(-), l(+)) is a bounded interval. It will be shown that the interaction strengths gamma(k) and the points z(k) 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.