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Mathematics & Statistics

Approximation Theory/Analysis (Leader: Prof. V. Totik)

Wednesday, April 17, 2002

Title
Speaker
Time
Place

Reproducing Kernels and Integral Operators Involving Orthogonal Polynomials
4:00pm-5:00pm
PHY 120

Wednesday, April 10, 2002

Title
Speaker
Time
Place

Products of Random Matrices: Limit Distributions
Arunava Mukherjea
3:00pm-4:00pm
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
Speaker
Time
Place

Interpolation in $$3$$-D
Boris Shekhtman
3:00pm-4:00pm
PHY 108

Wednesday, March 6, 2002

Title
Speaker
Time
Place

The Stieltjes-Wigert Moment Problem
Jacob Christiansen
3:00pm-4:00pm
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
Speaker

Time
Place

Zeros of Bergman Orthogonal Polynomials
Viktor Maymeskul
Vanderbilt University
3:00pm-4:00pm
PHY 108

Wednesday, February 6, 2002

Title
Speaker
Time
Place

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

Wednesday, January 30, 2002

Title
Speaker
Time
Place

Interpolating Spaces and Topology of Manifolds
Boris Shekhtman
3:00pm-4:00pm
PHY 120

Wednesday, January 16, 2002

Title
Speaker
Time
Place

Polynomial inverse images, or how to transfer results from one interval to compact sets
Vilmos Totik
3:00pm-4:00pm
PHY 120