Abstract
We analyze perturbations of the harmonic oscillator type operators in a Hilbert space \({\mathcal{H}}\), i.e. of the self-adjoint operator with simple positive eigenvalues μ k satisfying μ k+1 − μ k ≥ Δ > 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.
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Petr Siegl: On Leave From Nuclear Physics Institute ASCR.
PS appreciates the kind hospitality and support of OSU allowing his stays there in November 2012 and July 2013 and acknowledges the SCIEX Program; the work has been conducted within the SCIEX-NMS Fellowship, Project 11.263. Till March 2013, PS has been supported by a Grant within the scope of FCT’s project PTDC/ MAT/ 101007/2008 and partially by FCT’s projects PTDC/ MAT/ 101007/2008 and PEst-OE/MAT/UI0208/2011.
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Mityagin, B., Siegl, P. Root System of Singular Perturbations of the Harmonic Oscillator Type Operators. Lett Math Phys 106, 147–167 (2016). https://doi.org/10.1007/s11005-015-0805-7
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DOI: https://doi.org/10.1007/s11005-015-0805-7