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Эта публикация цитируется в 32 научных статьях (всего в 32 статьях)
Bispectrality of the Complementary Bannai–Ito Polynomials
Vincent X. Genesta, Luc Vineta, Alexei Zhedanovb a Centre de Recherches Mathématiques, Université de Montréal, C.P. 6128, Succursale Centre-ville, Montréal, Québec, Canada, H3C 3J7
b Donetsk Institute for Physics and Technology, Ukraine
Аннотация:
A one-parameter family of operators that have the complementary Bannai–Ito (CBI) polynomials as eigenfunctions is obtained. The CBI polynomials are the kernel partners of the Bannai–Ito polynomials and also correspond to a $q\rightarrow-1$ limit of the Askey–Wilson polynomials. The eigenvalue equations for the CBI polynomials are found to involve second order Dunkl shift operators with reflections and exhibit quadratic spectra. The algebra associated to the CBI polynomials is given and seen to be a deformation of the Askey–Wilson algebra with an involution. The relation between the CBI polynomials and the recently discovered dual $-1$ Hahn and para-Krawtchouk polynomials, as well as their relation with the symmetric Hahn polynomials, is also discussed.
Ключевые слова:
Bannai–Ito polynomials; quadratic algebras; Dunkl operators.
Поступила: 13 ноября 2012 г.; в окончательном варианте 27 февраля 2013 г.; опубликована 2 марта 2013 г.
Образец цитирования:
Vincent X. Genest, Luc Vinet, Alexei Zhedanov, “Bispectrality of the Complementary Bannai–Ito Polynomials”, SIGMA, 9 (2013), 018, 20 pp.
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/sigma801 https://www.mathnet.ru/rus/sigma/v9/p18
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