Root System of Singular Perturbations of the Harmonic Oscillator Type Operators

0458123 - ÚJF 2017 RIV NL eng J - Journal Article
Mityagin, B. - Siegl, Petr
Root System of Singular Perturbations of the Harmonic Oscillator Type Operators.
Letters in Mathematical Physics. Roč. 106, č. 2 (2016), s. 147-167. ISSN 0377-9017. E-ISSN 1573-0530
Institutional support: RVO:61389005
Keywords : non-self-adjoint operators * harmonic oscillator * Riesz basis * quadratic forms * singular petentials
Subject RIV: BE - Theoretical Physics
Impact factor: 1.671, year: 2016

We analyze perturbations of the harmonic oscillator type operators in a Hilbert space H, i.e. of the self-adjoint operator with simple positive eigenvalues mu(k) satisfying mu(k+1) - mu(k) >= Delta > 0. Perturbations are considered in the sense of quadratic forms. Under a local subordination assumption, the eigenvalues of the perturbed operator become eventually simple and the root system contains a Riesz basis.
Permanent Link: http://hdl.handle.net/11104/0258457