Friday, April 20, 2007
| Topic |
General weighted inequalities and their applications |
| Speaker |
Arcadii Grinshpan |
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.
Friday, April 13, 2007
| Topic |
Nonlinear extremal problems in Bergman spaces, II |
| Speaker |
Catherine Bénéteau |
Time |
1:00-2:00 p.m. |
| Place |
PHY 118 |
Friday, April 6, 2007
| Topic |
Nonlinear extremal problems in Bergman spaces |
| Speaker |
Catherine Bénéteau |
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.
Friday, March 30, 2007
| Topic |
Polynomials with prescribed zeros and small norm |
| Speaker |
Peter Varju
University of Szeged
Szeged, HUNGARY |
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.
Friday, March 23, 2007
| Topic |
Differentially-invariant linear spaces of multivariate polynomials |
| Speaker |
Wen-Xiu Ma |
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.
Friday, March 9, 2007
| Topic |
Analysis in Sub-Riemannian Spaces, Part II |
| Speaker |
Thomas Bieske |
Time |
1:00-2:00 p.m. |
| Place |
PHY 118 |
Friday, March 2, 2007
| Topic |
Analysis in Sub-Riemannian Spaces |
| Speaker |
Thomas Bieske |
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,ߪ,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.
Friday, February 9, 2007
| Topic |
Smooth Equilibrium Measures and Approximation |
| Speaker |
Vilmos Totik |
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.
Friday, February 2, 2007
| Topic |
Parametrization of Ideal Projections, Part II |
| Speaker |
Boris Shekhtman |
Time |
1:00-2:00 p.m. |
| Place |
PHY 118 |
Friday, January 26, 2007
| Topic |
Parametrization of Ideal Projections |
| Speaker |
Boris Shekhtman |
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.