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,...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Дата: | 2015 |
| Автори: | , , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2015
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/147130 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862560039070334976 |
|---|---|
| author | Álvarez López, J.A. Calaza, M. Franco, C. |
| author_facet | Álvarez López, J.A. Calaza, M. Franco, C. |
| 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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.
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| first_indexed | 2025-11-25T22:54:44Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-147130 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-25T22:54:44Z |
| publishDate | 2015 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Álvarez López, J.A. Calaza, M. Franco, C. 2019-02-13T17:16:09Z 2019-02-13T17:16:09Z 2015 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 https://nasplib.isofts.kiev.ua/handle/123456789/147130 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. The first author was partially supported by MICINN, Grants MTM2011-25656 and MTM2014-
 56950-P, and by Xunta de Galicia, Grant Consolidaci´on e estructuraci´on 2015 GPC GI-1574.
 The third author has received financial support from the Xunta de Galicia and the European
 Union (European Social Fund - ESF). en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications A Perturbation of the Dunkl Harmonic Oscillator on the Line Article published earlier |
| spellingShingle | A Perturbation of the Dunkl Harmonic Oscillator on the Line Álvarez López, J.A. Calaza, M. Franco, C. |
| title | 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_short | A Perturbation of the Dunkl Harmonic Oscillator on the Line |
| title_sort | perturbation of the dunkl harmonic oscillator on the line |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147130 |
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