| Speaker | Arcadii Grinshpan |
| Topic | General weighted inequalities and their applications |
| Time | 1:00-2:00 p.m. |
| Place | PHY 118 |
Abstract
We will discuss some weighted inequalities for complex vectors and complex-valued
functions.
Applications include: integral and coefficient convolutions; Borel-Laplace
transform; generalized hypergeometric series, special functions and orthogonal
polynomials; binomial coefficients; bi-Hermitian forms; integro-differential
inequalities; weighted norm inequalities; conformal mappings; entire functions
and formal power series.
| Speaker | Catherine Bénéteau |
| Topic | Nonlinear extremal problems in Bergman spaces, II |
| Time | 1:00-2:00 p.m. |
| Place | PHY 118 |
| Speaker | Catherine Bénéteau |
| Topic | Nonlinear extremal problems in Bergman spaces |
| Time | 1:00-2:00 p.m. |
| Place | PHY 118 |
Abstract
In this talk, I will survey a large class of nonlinear extremal problems in Hardy and Bergman spaces. I will discuss the general approach to such problems in Hardy spaces developed by S. Ya. Khavinson in the 60s and will talk about more recent results in Bergman spaces. Finally, I will formulate some "Kryz" type conjectures for non-vanishing functions in Bergman spaces.
| Speaker | Peter Varju University of Szeged Szeged, HUNGARY |
| Topic | Polynomials with prescribed zeros and small norm |
| Time | 1:00-2:00 p.m. |
| Place | PHY 118 |
Abstract
According to a result of Halasz there exist monic polynomials Pn of degree n such that they vanish at 1, and their supremum norm on the unit circle is < 1 + C/n. It immediatly follows that if we are given k < n1/2 points on the unit circle, then there is a polynomial Pn which vanishes at those points and |Pn(z)| < 1 + O(k2/n) for |z| = 1. We discuss the question if this estimate can be improved. Such polynomials are used in Turan's power sum method in number theory.
| Speaker | Wen-Xiu Ma |
| Topic | Differentially-invariant linear spaces of multivariate polynomials |
| Time | 1:00-2:00 p.m. |
| Place | PHY 118 |
Abstract
Motivated by a problem of Boris Shekhtman on existence of sub-spaces with special characteristics in two variables, we analyze sub-spaces of differentially-invariant linear spaces of multivariate polynomials and develop ways to extend given differentially-invariant linear spaces by creating new independent polynomials. This is a preliminary report.
| Speaker | Thomas Bieske |
| Topic | Analysis in Sub-Riemannian Spaces, Part II |
| Time | 1:00-2:00 p.m. |
| Place | PHY 118 |
| Speaker | Thomas Bieske |
| Topic | Analysis in Sub-Riemannian Spaces |
| Time | 1:00-2:00 p.m. |
| Place | PHY 118 |
Abstract
The Euclidean space Rn and a set of vector linearly independent vector fields X1,X2,...,Xm with m < n form a sub-Riemannian structure if the vector fields and their Lie brackets span Rn. Two classic examples of such spaces include the Heisenberg group, which possesses an algebraic group law, and Grushin spaces, which do not. We will examine these spaces in terms of geometry, potential theory and partial differential equations.
| Speaker | Vilmos Totik |
| Topic | Smooth Equilibrium Measures and Approximation |
| Time | 1:00-2:00 p.m. |
| Place | PHY 118 |
Abstract
Approximation by weighted polynomials where the weight changes with the degree has been thoroughly investigated in the last two decades. This talk will present the problem, its history, its relation to potential theory, and a recent breakthrough which solves the problem completely.
| Speaker | Boris Shekhtman |
| Topic | Parametrization of Ideal Projections, Part II |
| Time | 1:00-2:00 p.m. |
| Place | PHY 118 |
| Speaker | Boris Shekhtman |
| Topic | Parametrization of Ideal Projections |
| Time | 1:00-2:00 p.m. |
| Place | PHY 118 |
Abstract
We develop a system of parameters that describe a family of ideal projections in two variables and show that no such system exists in three or more variables. These results are motivated (and are equivalent to) one problem of Carl de Boor.
Please direct questions to mthmaster@nosferatu.cas.usf.edu.
Last updated: 2007-04-09.
Copyright © 2000, USF Department of Mathematics & Statistics.