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Mathematics & Statistics

# Analysis (Leader: Prof. Boris Shekhtman )

## Friday, April 15, 2005

Title
Speaker
Time
Place

Absolute Minimizers on Carnot Groups
Thomas Bieske
5:00pm-6:00pm
PHY 120

Abstract

Aronsson (1967) first considered the problem of canonically extending a Lipschitz function on the boundary of a domain in $$\mathbb{R}^n$$ into the whole domain without raising the Lipschitz constant. This problem was solved by R. Jensen (1993). We consider the same problem in a class of non-abelian groups, called Carnot groups, which are also non-isotropic metric spaces.

In addition, properties of such minimizers are discussed.

## Friday, February 25, 2005

Title
Speaker

Time
Place

Generalizations of Chebyshev Polynomials and Polynomial Mappings
James Griffin
University of Central Florida
5:00pm-6:00pm
PHY 120

Abstract

Generalized Chebyshev Polynomials orthogonal on two disjoint intervals have a representation in terms of elliptic functions. I will present the general case on several intervals and discuss their application to inverse images of a single interval under a polynomial mapping. I will also discuss some recent results on further generalizations of the classical orthogonal polynomials to the several interval case.

## Friday, February 18, 2005

Title
Speaker
Time
Place

How come $$1+1=3$$?
Wen-Xiu Ma
5:00pm-6:00pm
PHY 120

## Friday, February 11, 2005

Title
Speaker

Time
Place

Plancherel-Rotach asymptotics for $$q$$-orthogonal polynomials and a $$q$$-Airy function
Mourad Ismail
University of Central Florida
5:00pm-6:00pm
PHY 120

## Friday, February 4, 2005

Title
Speaker
Time
Place

Algebra of Approximation: Introductory overview
Boris Shekhtman
5:00pm-6:00pm
PHY 120

Abstract

This seems to be a hot new topic with many possibilities for interesting discoveries in Analysis and Algebraic Geometry.