A Perturbation of the Dunkl Harmonic Oscillator on the Line
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...
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Інститут математики НАН України
2015
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| Schriftenreihe: | Symmetry, Integrability and Geometry: Methods and Applications |
| Online Zugang: | http://dspace.nbuv.gov.ua/handle/123456789/147130 |
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| 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. |
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irk-123456789-1471302019-02-14T01:23:24Z A Perturbation of the Dunkl Harmonic Oscillator on the Line Álvarez López, J.A. Calaza, M. Franco, C. 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 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. 2015 Article 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 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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DSpace DC |
| language |
English |
| description |
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 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. |
| format |
Article |
| author |
Álvarez López, J.A. Calaza, M. Franco, C. |
| spellingShingle |
Álvarez López, J.A. Calaza, M. Franco, C. A Perturbation of the Dunkl Harmonic Oscillator on the Line Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Álvarez López, J.A. Calaza, M. Franco, C. |
| author_sort |
Álvarez López, J.A. |
| title |
A Perturbation of the Dunkl Harmonic Oscillator on the Line |
| title_short |
A Perturbation of the Dunkl Harmonic Oscillator on the Line |
| title_full |
A Perturbation of the Dunkl Harmonic Oscillator on the Line |
| title_fullStr |
A Perturbation of the Dunkl Harmonic Oscillator on the Line |
| title_full_unstemmed |
A Perturbation of the Dunkl Harmonic Oscillator on the Line |
| title_sort |
perturbation of the dunkl harmonic oscillator on the line |
| publisher |
Інститут математики НАН України |
| publishDate |
2015 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/147130 |
| citation_txt |
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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
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2025-07-11T01:25:01Z |
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