Singular Schrodinger operators with prescribed spectral properties

0552559 - ÚJF 2023 RIV US eng J - Journal Article
Behrndt, J. - Khrabustovskyi, Andrii
Singular Schrodinger operators with prescribed spectral properties.
Journal of Functional Analysis. Roč. 282, č. 1 (2022), č. článku 109252. ISSN 0022-1236. E-ISSN 1096-0783
R&D Projects: GA ČR(CZ) GA21-07129S
Institutional support: RVO:61389005
Keywords : Schrodinger operator * delta-Interaction * Essential spectrum * Discrete spectrum
OECD category: Pure mathematics
Impact factor: 1.7, year: 2022
Method of publishing: Open access
https://doi.org/10.1016/j.jfa.2021.109252

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.
Permanent Link: http://hdl.handle.net/11104/0327666