Plamen Iliev
Orthogonality relations for bivariate Bernstein-Szeg\H{o} measures.
Mon, 11/28/2011 - 15:01 — SomNambulAuthors: Plamen Iliev, Greg Knese, Jeffrey S. Geronimo
Subjects: Complex Variables
AbstractThe orthogonality properties of certain subspaces associated with bivariate
Bernstein-Szeg\H{o} measures are considered. It is shown that these spaces
satisfy more orthogonality relations than expected from the relations that
define them. The results are used to prove a Christoffel-Darboux like formula
for these measures.The Rahman polynomials and the Lie algebra sl_3(C).
Tue, 06/29/2010 - 15:01 — SomNambulAuthors: Plamen Iliev, Paul Terwilliger
Subjects: Representation Theory
AbstractWe interpret the Rahman polynomials in terms of the Lie algebra $sl_3(C)$.
Using the parameters of the polynomials we define two Cartan subalgebras for
$sl_3(C)$, denoted $H$ and $\tilde{H}$. We display an antiautomorphism
$\dagger$ of $sl_3(C)$ that fixes each element of $H$ and each element of
$\tilde{H}$.Bispectral commuting difference operators for multivariable Askey-Wilson polynomials.
Mon, 08/17/2009 - 18:30 — SomNambulAuthors: Plamen Iliev
Subjects: Classical Analysis and ODEs
AbstractWe construct a commutative algebra A_z, generated by d algebraically
independent q-difference operators acting on variables z_1, z_2,..., z_d, which
is diagonalized by the multivariable Askey-Wilson polynomials P_n(z) considered
by Gasper and Rahman [6]. Iterating Sears' transformation formula, we show that
the polynomials P_n(z) possess a certain duality between z and n.
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