# Research

## Analysis

### Friday, November 5, 2004

Speaker 1: Qiyu Sun, University of Central Florida
Title: Wiener Lemma and Average Sampling
Speaker 2: Vilmos Totik
Title: Polynomial approximation with varying weights
Time: 4:15pm–6:00pm
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

Title: Problems in the theory of boundary behavior of analytic functions and F. and M. Riesz Theorem
Speaker: Arthur Danielyan
Time: 5:00pm–6:00pm
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

Title: Interpolation Projections and Polynomial Ideals
Speaker: Boris Shekhtman
Time: 5:00pm–6:00pm
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

Title: Zeros of orthogonal polynomials on the circle
Speaker: Vilmos Totik
Time: 5:00pm–6:00pm
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.