A Perturbation of the Dunkl Harmonic Oscillator on the Line

• Veröffentlicht in: Symmetry, Integrability and Geometry: Methods and Applications
• Datum: 2015
• Hauptverfasser: Álvarez López, J.A., Calaza, M., Franco, C.
• Format: Artikel
• Sprache: English
• Veröffentlicht: Інститут математики НАН України 2015
• Online Zugang: https://nasplib.isofts.kiev.ua/handle/123456789/147130
• Назва журналу: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Zitieren: A Perturbation of the Dunkl Harmonic Oscillator on the Line / J.A. Álvarez López, M. Calaza, C. Franco // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 28 назв. — англ.

Let Jσ be the Dunkl harmonic oscillator on R (σ>−1/2. For 0<u<1 and ξ>0, it is proved that, if σ>u−1/2, then the operator U=Jσ+ξ|x|⁻²u, with appropriate domain, is essentially self-adjoint in L²(R,|x|²σdx), the Schwartz space S is a core of Ū¹/², and Ū has a discrete spectrum, which i...