Splinter Group:
Operator Theory and Real Analysis

Organizer: James Cruickshank (NUI Galway)

All talks will be held in the Cairnes Lecture Theatre.

This splinter group follows the Analysis Special Session on both afternoons.

Tuesday, April 7 2009

16:30 - 17:00

Sam Elliott (University of Leeds):
Composition Operators on the Half Plane

17:00 - 17:30

Olga Maleva (University of Birmingham):
Exceptional sets of Lipschitz functions

A theorem of Lebesgue says that a subset of the real line has measure 0 if and only if some Lipschitz function is not differentiable anywhere in this set. But in higher dimensions, whilst the "if" part is still true, there exist exceptional sets of measure 0 such that every Lipschitz function is differentiable on a dense subset of the set. I will show that such sets can even be compact and of Hausdorff dimension 1. I will explain why this is a step towards a solution of a long-standing open problem in geometric measure theory.

Wednesday, April 8 2009

16:30 - 17:00

Stephen Wills (UCC):
Projection-valued operator stochastic cocycles

In the classification of endomorphism semigroups by Arveson, Powers et al, one class of objects of recent interest are projection-valued cocycles, used for perturbation purposes. I will discuss these twisted versions of one-parameter semigroups from the point of view of quantum stochastic calculus.

17:00 - 17:30

James Cruickshank (NUI Galway):
A polarization formula for forward differences

In their foundational paper, published in 1934, Mazur and Orlicz showed (among other things) that generalised polynomial functions of degree n can be characterised as those functions that have vanishing (n+1)^{th} order pure forward differences. We will present a generalization of one of the key theorems of that paper. Our result may be thought of as a polarization formula for forward differences, analogous to the well known polarization formulae that relate polynomials to symmetric multilinear forms.