## Geometry Seminar - Abstracts

### Talk

Wednesday 18 April 2018, 16:00-17:00 in HG03.085

**Erdal Emsiz** (Pontificia Universidad Catolica de Chile)

*Discrete Fourier transforms and cubature rules*

### Abstract

The Bernstein-Szegö polynomials are a multi-parameter family of
orthogonal polynomials generalizing the Chebyshev polynomials. It is
well-known that they diagonalize a family of semi-infinite Jacobi
matrices. In this talk, based on recent joint work with Jan Felipe van
Diejen, we will explain how to glue two such families of
Bernstein-Szegö polynomials so as to diagonalize a corresponding
family of finite Jacobi matrices. The symmetry of the finite Jacobi
matrix gives rise to a finite-dimensional system of discrete
orthogonal relations for the pertinent composite eigenbasis built of
Bernstein-Szegö polynomials. We will indicate how these relations
imply Gauss-type quadrature. We will also discuss multivariate
versions, in particular cubature rules for the exact integration of
symmetric rational functions with prescribed poles.

(

Back to geometry seminar schedule)