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Title: Reproducing Kernels and Integral Operators Involving Orthogonal Polynomials Speaker: Mourad Ismail Time: 4:00pm–5:00pm Place: PHY 120
Title: Products of Random Matrices: Limit Distributions Speaker: Arunava Mukherjea Time: 3:00pm–4:00pm Place: PHY 120
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.
Title: Interpolation in \(3\)-D Speaker: Boris Shekhtman Time: 3:00pm–4:00pm Place: PHY 108
Title: The Stieltjes-Wigert Moment Problem Speaker: Jacob Christiansen Time: 3:00pm–4:00pm Place: PHY 120
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.
Title: Zeros of Bergman Orthogonal Polynomials Speaker: Viktor Maymeskul, Vanderbilt University Time: 3:00pm–4:00pm Place: PHY 108
Title: Soliton, Positon and Complexiton Solutions to the KdV Equation Speaker: Wen-Xiu Ma Time: 3:00pm–4:00pm Place: PHY 120
Title: Interpolating Spaces and Topology of Manifolds Speaker: Boris Shekhtman Time: 3:00pm–4:00pm Place: PHY 120
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