Speaker
Description
On two integer lattices with interlacing nodes let us introduce two discrete measures for which a point weight is determined by the product of two classical Meixner weights. It turns out that the resulting measures are positive when the lattices alternate.
This generalisation of the Meixner weight was introduced by Sorokin in 2010. He studied asymptotic behaviour of the corresponding orthogonal polynomials~$P_{n,n}$ with diagonal indices. The orthogonal polynomials may be constructed using the (discrete) Rodrigues formula, but the question whether they are uniquely defined remained open.
Indeed, such a system of measures does not form a Nikishin system as the measures have disjoint supports; it does not form an Angelesco systems either since one of these supports lies in the convex hull of the other.
Nevertheless, the uniqueness of the orthogonal polynomials (i.e. the normality of diagonal indices for Sorokin's system of measures) would be useful for applying Sorokin's result.
The talk will be aimed at showing that this system of measures is perfect (that is all indices are normal). In the course of our proof we derive an intriguing hypergeometric identity. We also rely on an extension of the aforementioned Rodrigues formula.
This is a joint research with Alexander Aptekarev and Vladimir Lysov.
