Friday, November 5, 2004
| Topic |
Wiener Lemma and Average Sampling |
| Speaker 1 |
Qiyu Sun
University of Central Florida |
| Speaker 2 |
Vilmos Totik |
| Topic |
Polynomial approximation with varying weights |
| Time |
4:15-6:00 p.m. |
| Place |
MAP 233 |
Note: This week, the seminar is joint with the Department of
Mathematics at the University of Central Florida and will be held in Orlando.
Friday, October 8, 2004
| Topic |
Problems in the theory of boundary behavior of analytic functions and F. and M. Riesz Theorem |
| Speaker |
Dr. Arthur Danielyan |
| Time |
5:00-6:00 p.m. |
| Place |
PHY 130 |
Abstract
Some problems and new results in boundary behavior of analytic functions will
be discussed based on certain new association of a few well known classical
results. A new simple proof of the boundary uniqueness theorem of F. and M.
Riesz will be presented.
Friday, September 24, 2004
| Topic |
Interpolation Projections and Polynomial Ideals |
| Speaker |
Professor Boris Shekhtman |
| Time |
5:00-6:00 p.m. |
| Place |
PHY 130 |
Abstract
There is an interesting relation between interpolation projections, ideals of
polynomials, resulting algebraic varieties and solutions of homogeneous DE with
constant coefficients. These relationships are completely understood for
polynomials of one variables. In my talk I will explore some known (and unknown)
analogues for several variables. Hence the talk will contain a mixture of
approximation theory, algebraic geometry and PDEs.
Friday, September 16, 2004
| Topic |
Zeros of orthogonal polynomials on the circle |
| Speaker |
Professor Vilmos Totik |
| Time |
5:00-6:00 p.m. |
| Place |
PHY 130 |
Abstract
It is shown (in joint work with Barry Simon), that there is a universal measure
on the circle such that any probability measure on the unit disk is the limit of
zero distribution of some subsequence of the corresponding orthogonal polynomials.
This answers in a very strong sense a problem of Turán. The result is
obtained by showing that one can freely prescribe the n-th orthogonal
polynomial and N-n zeros of the N-th one. This is
obtained by calculating the topological degree of a related mapping.