Departmental Colloquium
Calixto Calderon
UIC
The Watson Kernel and Summability of Fourier-Jacobi series
Abstract: Series of Jacobi Orthogonal Polynomials is always a hot topic in Analysis.
In this lecture I will discuss some not very well known facts, namely, the
two versions for the Poisson Kernel of the Abel Summability of Jacobi
Series. The versions I refer to are the Watson and Bailey kernels. The use
of the Watson form provides good localization results. A theory of
Mukenhoupt weights will be discussed in the context of localization
results. The Bailey's form is nonnegative, and therefore it provides
simple proofs of the norm approximations of the Abel sums. A comment on
early results will be provided.
Friday April 1, 2011 at 3:00 PM in SEO 636