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Mirror symmetric polynomials orthogonal on the unit circle
Alexei Zhedanov
We introduce and study a special family of polynomials orthogonal on the unit circle (OPUC). These OPUC satisfy a mirror symmetry property of their Verblunsky coefficients. Several…
Algebraic interpretation of the two-variable Jacobi polynomials on the triangle: the pentagonal way
Nicolas Crampé, Quentin Labriet, Lucia Morey +3
The rank two Jacobi algebra is used to provide an interpretation of the two-variable Jacobi polynomials on the triangle, as overlaps betwee…
The rank two Jacobi algebra
Nicolas Crampe, Satoshi Tsujimoto, Luc Vinet +1
The quadratic rank two Jacobi algebra is identified from the relations obeyed by the bispectral operators of the two variable Jacobi polynomials orthogonal on the triangle. It is s…
Eigenvalue equations for sieved polynomials or proving Askey right again
Luc Vinet, Alexei Zhedanov
The sieved Jacobi polynomials have been introduced by Askey. These can be obtained from conveniently taking to be a root of unity in the Askey-Wilson polynomials. The question…
Algebras behind the bispectrality of the Wilson rational functions and their limits
Nicolas Crampe, Satoshi Tsujimoto, Luc Vinet +1
The properties of the Wilson rational functions with three different normalizations are described. For one normalization, it satisfies an recurrence relation,…
Bispectrality of the sieved Jacobi polynomials
Luc Vinet, Alexei Zhedanov
It is shown that the CMV Laurent polynomials associated to the sieved Jacobi polynomials on the unit circle satisfy an eigenvalue equation with respect to a first order differentia…