Root System of Singular Perturbations of the Harmonic Oscillator Type Operators

Boris Mityagin; Petr Siegl

doi:10.1007/s11005-015-0805-7

Root System of Singular Perturbations of the Harmonic Oscillator Type Operators

Boris Mityagin, Petr Siegl^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

We analyze perturbations of the harmonic oscillator type operators in a Hilbert space $${\mathcal{H}}$$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.

Original language	English
Pages (from-to)	147-167
Number of pages	21
Journal	Letters in Mathematical Physics
Volume	106
Issue number	2
DOIs	https://doi.org/10.1007/s11005-015-0805-7
Publication status	Published - 1 Feb 2016
Externally published	Yes

Keywords

harmonic oscillator
non-self-adjoint operators
quadratic forms
Riesz basis
singular potentials

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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10.1007/s11005-015-0805-7

Cite this

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title = "Root System of Singular Perturbations of the Harmonic Oscillator Type Operators",

abstract = "We analyze perturbations of the harmonic oscillator type operators in a Hilbert space $${\mathcal{H}}$$H, i.e. of the self-adjoint operator with simple positive eigenvalues μk satisfying μk+1 − μk ≥ 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.",

keywords = "harmonic oscillator, non-self-adjoint operators, quadratic forms, Riesz basis, singular potentials",

author = "Boris Mityagin and Petr Siegl",

note = "Funding Information: 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{\textquoteright}s project PTDC/ MAT/ 101007/2008 and partially by FCT{\textquoteright}s projects PTDC/ MAT/ 101007/2008 and PEst-OE/MAT/UI0208/2011. Publisher Copyright: {\textcopyright} 2015, Springer Science+Business Media Dordrecht.",

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N2 - We analyze perturbations of the harmonic oscillator type operators in a Hilbert space $${\mathcal{H}}$$H, i.e. of the self-adjoint operator with simple positive eigenvalues μk satisfying μk+1 − μk ≥ 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.

AB - We analyze perturbations of the harmonic oscillator type operators in a Hilbert space $${\mathcal{H}}$$H, i.e. of the self-adjoint operator with simple positive eigenvalues μk satisfying μk+1 − μk ≥ 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.

KW - harmonic oscillator

KW - non-self-adjoint operators

KW - quadratic forms

KW - Riesz basis

KW - singular potentials

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Root System of Singular Perturbations of the Harmonic Oscillator Type Operators

Abstract

Keywords

ASJC Scopus subject areas

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