Approximation Theory/Analysis
(Leader: Prof. V. Totik)
Wednesday, April 17, 2002
| Topic |
Reproducing Kernels and Integral Operators Involving Orthogonal Polynomials |
| Speaker |
Mourad Ismail |
| Time |
4:00-5:00 p.m. |
| Place |
PHY 120 |
Wednesday, April 10, 2002
| Topic |
Products of Random Matrices: Limit Distributions |
| Speaker |
Arunava Mukherjea |
| Time |
3:00-4:00 p.m. |
| 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
| Topic |
Interpolation in 3D |
| Speaker |
Boris Shekhtman |
| Time |
3:00-4:00 p.m. |
| Place |
PHY 108 |
Wednesday, March 6, 2002
| Topic |
The Stieltjes-Wigert Moment Problem |
| Speaker |
Jacob Christiansen |
| Time |
3:00-4:00 p.m. |
| 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
| Topic |
Zeros of Bergman Orthogonal Polynomials |
| Speaker |
Dr. Viktor Maymeskul
Vanderbilt University |
| Time |
3:00-4:00 p.m. |
| Place |
PHY 108 |
Wednesday, February 6, 2002
| Topic |
Soliton, Positon and Complexiton Solutions to the KdV Equation |
| Speaker |
Dr. Wen-Xiu Ma |
| Time |
3:00-4:00 p.m. |
| Place |
PHY 120 |
Wednesday, January 30, 2002
| Topic |
Interpolating Spaces and Topology of Manifolds |
| Speaker |
Professor Boris Shekhtman |
| Time |
3:00-4:00 p.m. |
| Place |
PHY 120 |
Wednesday, January 16, 2002
| Topic |
Polynomial inverse images, or how to transfer results from one interval to compact sets |
| Speaker |
Professor Vilmos Totik |
| Time |
3:00-4:00 p.m. |
| Place |
PHY 120 |