GT ADG-Systèmes Dynamiques

About a class of orthogonal polynomials with unbounded recurrence coefficients

by Mr Bartosz Trojan (Académie des Sciences de Pologne et École Polytechnique de Wroclaw-INVITÉ CNRS IDP)

pticrème (Orléans institut Denis Poisson)


Orléans institut Denis Poisson

In this talk we introduce a class of orthogonal polynomials with N-periodically modulated Jacobi parameters.
The class is sufficiently large to contain many classical polynomials such as Hermite, Meixner—Pollaczek, Laguerre.
We implement a program in which we study convergence of generalized Tur\'an determinants, approximation of the density of
the orthogonality measure, uniform asymptotic behavior of orthogonal polynomials as well as Christoffel--Darboux kernels.
We also study the asymptotic distribution of zeros. The talk is based on joint works with Grzegorz Świderski (Polish
Academy of Sciences & University of Wroclaw).