The Askey-Wilson polynomials and q-Sturm-Lioville problems
B. Malcolm Brown, William Desmond Evans, Mourad E. H. Ismail
Abstract
We find the adjoint of the Askey-Wilson divided difference operator with respect to the inner procuct on L2(-1,1,(1-x2)-1/2 dx) defined as a Cauchy principle value and show that the Askey-Wilson polynomials are solutions of a q-Sturm-Liouville problem. From these facts we deduce various properties of the polynomials in a simple and straightforward way. We also provide an operator theoretic description of the Askey-Wilson operator.
Create a lesson
Related papers
Characterizing higher-dimensional Hölder domains via spherical geometric functions
Emily Casey, Max Engelstein, Tatiana Toro
The second type of power mean bounds for the hypergeometric mean
Zhen-Hang Yang, Jing-Feng Tian
Spread-out Furstenberg sets II: general configurations and fractal restricted projections
Alex Cohen, Pablo Shmerkin, Hong Wang et al.
Spread-out Furstenberg sets I: the sticky case
Tuomas Orponen, Pablo Shmerkin
Hsiang cubics as spherical Chebyshev polynomials: equioscillation and idempotent quadrature
Vladimir G. Tkachev
Sharp power-weight estimates for the fractional spherical maximal operator
Riju Basak, Surjeet Singh Choudhary, Chun-Yen Shen et al.