Наукова електронна бібліотека
періодичних видань НАН України
періодичних видань НАН України
Spectral Analysis of Certain Schrödinger Operators
Репозиторій DSpace/Manakin
- Домашня сторінка
- →
- Фізико-технічні та математичні науки
- →
- Відділення математики
- →
- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
- →
- Symmetry, Integrability and Geometry: Methods and Applications, 2012, том 8
- →
- Symmetry, Integrability and Geometry: Methods and Applications, 2012, том 8, випуск за цей рік
- →
- Переглянути статтю
JavaScript is disabled for your browser. Some features of this site may not work without it.
Spectral Analysis of Certain Schrödinger Operators
Інший ID:
2010 Mathematics Subject Classification: 30E05; 33C45; 39A10; 42C05; 44A60
DOI: http://dx.doi.org/10.3842/SIGMA.2012.061
DOI: http://dx.doi.org/10.3842/SIGMA.2012.061
Посилання:
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.
Підтримка:
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.
Дата:
2012
Переглядів:
454
Завантажень:
230
Анотація:
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].
