Наукова електронна бібліотека
періодичних видань НАН України
періодичних видань НАН України
Raising and Lowering Operators for Askey-Wilson Polynomials
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, 2007, том 3
- →
- Symmetry, Integrability and Geometry: Methods and Applications, 2007, том 3, випуск за цей рік
- →
- Переглянути статтю
JavaScript is disabled for your browser. Some features of this site may not work without it.
Raising and Lowering Operators for Askey-Wilson Polynomials
Інший ID:
2000 Mathematics Subject Classification: 33D45; 33D52; 33D80
Посилання:
Raising and Lowering Operators for Askey-Wilson Polynomials / S. Sahi // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 25 назв. — англ.
Підтримка:
This paper is a contribution to the Vadim Kuznetsov Memorial Issue “Integrable Systems and Related Topics”. We would like to thank the (anonymous) referee for several insightful suggestions which have improved the paper considerably. The referee has also pointed out that one can give an alternative proof of formulas (17) and (18) by combining Theorem 1 with the following identity relating the operators D and D`:
[(1 − q²)D`z + q²D(z + z⁻¹) − q(z + z⁻¹)D] f
= (1 − q) [(e₁ − e₃) − (1 − abcd)(z + z⁻¹)] f,
which holds for all symmetric Laurent polynomials.
Дата:
2007
Переглядів:
552
Завантажень:
300
Анотація:
In this paper we describe two pairs of raising/lowering operators for Askey-Wilson polynomials, which result from constructions involving very different techniques. The first technique is quite elementary, and depends only on the ''classical'' properties of these polynomials, viz. the q-difference equation and the three term recurrence. The second technique is less elementary, and involves the one-variable version of the double affine Hecke algebra.
