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math.QA2012★ 8 cited
Bispectral extensions of the Askey-Wilson polynomials
Plamen Iliev
Following the pioneering work of Duistermaat and Grünbaum, we call a family of polynomials bispectral, if the polynomials are simultaneously eigenfuncti…
math.CV2012★ 9 cited
Fejér-Riesz factorizations and the structure of bivariate polynomials orthogonal on the bi-circle
Jeffrey S. Geronimo, Plamen Iliev
We give a complete characterization of the positive trigonometric polynomials Q(θ,ϕ) on the bi-circle, which can be factored as Q(θ,ϕ)=|p(e^{iθ},e^{iϕ})|^2 where p(z,w) is a polyno…