# Research

## Analysis

### Wednesday, April 17, 2002

Title: Reproducing Kernels and Integral Operators Involving Orthogonal Polynomials
Time: 4:00pm–5:00pm
Place: PHY 120

### Wednesday, April 10, 2002

Title: Products of Random Matrices: Limit Distributions
Speaker: Arunava Mukherjea
Time: 3:00pm–4:00pm
Place: PHY 120

#### Abstract

The subject of this talk is weak convergence for products of $$d\times d$$ random matrices. Approximation through measures with finite support will be useful. Connection with a classical (still open) problem of Erdös will be pointed out.

### Wednesday, March 20, 2002

Title: Interpolation in $$3$$-D
Speaker: Boris Shekhtman
Time: 3:00pm–4:00pm
Place: PHY 108

### Wednesday, March 6, 2002

Title: The Stieltjes-Wigert Moment Problem
Speaker: Jacob Christiansen
Time: 3:00pm–4:00pm
Place: PHY 120

#### Abstract

The very first examples of indeterminate moment problems were given by Stieltjes in his famous memoir from 1894-95. For instance, he pointed out that the density of the log-normal distribution belongs to an indeterminate moment problem and the corresponding orthogonal polynomials were found by Wigert in 1923. In a paper from 1970, Chihara observed that the log-normal density satisfy a simple functional equation. Our starting point will be the functional equation $$f(xq)=xf(x)$$, $$x>0$$. We construct a transformation of the set of solutions which has all the classical solutions as fixed points, but not the so-called $$N$$-extremal solution. The iterated action of this transformation starting at a certain $$N$$-extremal solution can be found explicitly. In the limit one ends up with two well-known solutions found by Berg in 1998, and this result brings the Nevalinna parametrization into focus.

### Tuesday, February 12, 2002

Title: Zeros of Bergman Orthogonal Polynomials
Speaker: Viktor Maymeskul, Vanderbilt University
Time: 3:00pm–4:00pm
Place: PHY 108

### Wednesday, February 6, 2002

Title: Soliton, Positon and Complexiton Solutions to the KdV Equation
Speaker: Wen-Xiu Ma
Time: 3:00pm–4:00pm
Place: PHY 120

### Wednesday, January 30, 2002

Title: Interpolating Spaces and Topology of Manifolds
Speaker: Boris Shekhtman
Time: 3:00pm–4:00pm
Place: PHY 120

### Wednesday, January 16, 2002

Title: Polynomial inverse images, or how to transfer results from one interval to compact sets
Speaker: Vilmos Totik
Time: 3:00pm–4:00pm
Place: PHY 120