Spectral Analysis of Certain Schrödinger Operators
The J-matrix method is extended to difference and q-difference operators and is applied to several explicit differential, difference, q-difference and second order Askey-Wilson type operators. The spectrum and the spectral measures are discussed in each case and the corresponding eigenfunction expan...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2012 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2012
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/148463 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Spectral Analysis of Certain Schrödinger Operators / Mourad E.H. Ismail, E. Koelink // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 40 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862712124845850624 |
|---|---|
| author | Ismail, Mourad E.H. Koelink, E |
| author_facet | Ismail, Mourad E.H. Koelink, E |
| citation_txt | Spectral Analysis of Certain Schrödinger Operators / Mourad E.H. Ismail, E. Koelink // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 40 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | The J-matrix method is extended to difference and q-difference operators and is applied to several explicit differential, difference, q-difference and second order Askey-Wilson type operators. The spectrum and the spectral measures are discussed in each case and the corresponding eigenfunction expansion is written down explicitly in most cases. In some cases we encounter new orthogonal polynomials with explicit three term recurrence relations where nothing is known about their explicit representations or orthogonality measures. Each model we analyze is a discrete quantum mechanical model in the sense of Odake and Sasaki [J. Phys. A: Math. Theor. 44 (2011), 353001, 47 pages].
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| first_indexed | 2025-12-07T17:34:31Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-148463 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T17:34:31Z |
| publishDate | 2012 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Ismail, Mourad E.H. Koelink, E 2019-02-18T13:10:40Z 2019-02-18T13:10:40Z 2012 Spectral Analysis of Certain Schrödinger Operators / Mourad E.H. Ismail, E. Koelink // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 40 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 30E05; 33C45; 39A10; 42C05; 44A60 DOI: http://dx.doi.org/10.3842/SIGMA.2012.061 https://nasplib.isofts.kiev.ua/handle/123456789/148463 The J-matrix method is extended to difference and q-difference operators and is applied to several explicit differential, difference, q-difference and second order Askey-Wilson type operators. The spectrum and the spectral measures are discussed in each case and the corresponding eigenfunction expansion is written down explicitly in most cases. In some cases we encounter new orthogonal polynomials with explicit three term recurrence relations where nothing is known about their explicit representations or orthogonality measures. Each model we analyze is a discrete quantum mechanical model in the sense of Odake and Sasaki [J. Phys. A: Math. Theor. 44 (2011), 353001, 47 pages]. The research of Mourad E.H. Ismail is supported by a Research Grants Council of Hong Kong under contract # 101411 and NPST Program of King Saud University, Saudi Arabia, 10-MAT 1293-02. This work was also partially supported by a grant from the ‘Collaboration Hong Kong –Joint Research Scheme’ sponsored by the Netherlands Organisation of Scientific Research and the Research Grants Council for Hong Kong (Reference number: 600.649.000.10N007). The work for this paper was done while both authors visited City University Hong Kong, and we are grateful for the hospitality.
 We thank Luc Vinet and Hocine Bahlouli for useful comments and references. We also thank the referees for their very careful reading and for their suggestions and constructive criticism that have improved the paper. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Spectral Analysis of Certain Schrödinger Operators Article published earlier |
| spellingShingle | Spectral Analysis of Certain Schrödinger Operators Ismail, Mourad E.H. Koelink, E |
| title | Spectral Analysis of Certain Schrödinger Operators |
| title_full | Spectral Analysis of Certain Schrödinger Operators |
| title_fullStr | Spectral Analysis of Certain Schrödinger Operators |
| title_full_unstemmed | Spectral Analysis of Certain Schrödinger Operators |
| title_short | Spectral Analysis of Certain Schrödinger Operators |
| title_sort | spectral analysis of certain schrödinger operators |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/148463 |
| work_keys_str_mv | AT ismailmouradeh spectralanalysisofcertainschrodingeroperators AT koelinke spectralanalysisofcertainschrodingeroperators |