Sobolev orthogonal polynomials in several variables

Analysis Seminar
Wednesday, August 26, 2015 - 2:05pm for 1 hour (actually 50 minutes)
Skiles 005
Lidia Fernandez – Applied Math Dept, University of Granada
Jeff Geronimo
The purpose of this talk is to introduce some recent works on the field of Sobolev orthogonal polynomials. I will mainly focus on our two last works on this topic. The first has to do with orthogonal polynomials on product domains. The main result shows how an orthogonal basis for such an inner product can be constructed for certain weight functions, in particular, for product Laguerre and product Gegenbauer weight functions. The second one analyzes a family of mutually orthogonal polynomials on the unit ball with respect to an inner product which involves the outward normal derivatives on the sphere. Using the representation of these polynomials in terms of spherical harmonics, algebraic and analytic properties will be deduced. First, we will get connection formulas relating classical multivariate orthogonal polynomials on the ball with our family of Sobolev orthogonal polynomials. Then explicit expressions for the norms will be obtained, among other properties.