Date & Time: Tuesday, March 17, 2009, 16:30-17:30.
Venue: Ramanujan Hall

Title: Bezoutians, Euclidean Algorithm and Orthogonal Polynomials

Speaker: Piotr Pragacz, Polish Academy of Sciences

Abstract: We prove a quadratic expression for the Bezoutian of two univariate polynomials in terms of the remainders for the Euclidean algorithm. In case of two polynomials of the same degree, or of consecutive degrees, this allows us to interpret their Bezoutian as the Christoffel-Darboux kernel for a finite family of orthogonal polynomials, arising from the Euclidean algorithm. We give orthogonality properties of remainders, and reproducing properties of Bezoutians.