A Perturbation of the Dunkl Harmonic Oscillator on the Line
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
A Perturbation of the Dunkl Harmonic Oscillator on the Line
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| Creator |
Álvarez López, J.A.
Calaza, M. Franco, C. |
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| Description |
Let Jσ be the Dunkl harmonic oscillator on R (σ>−1/2. For 00, 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 is estimated in terms of the spectrum of Ĵσ. A generalization Jσ,τ of Jσ is also considered by taking different parameters σ and τ on even and odd functions. Then extensions of the above result are proved for Jσ,τ, where the perturbation has an additional term involving, either the factor x⁻¹ on odd functions, or the factor x on even functions. Versions of these results on R+ are derived.
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| Date |
2019-02-13T17:16:09Z
2019-02-13T17:16:09Z 2015 |
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| Type |
Article
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| Identifier |
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.
1815-0659 2010 Mathematics Subject Classification: 47A55; 47B25; 33C45 DOI:10.3842/SIGMA.2015.059 http://dspace.nbuv.gov.ua/handle/123456789/147130 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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