F-differentiable functions and F-quasianalyticity

Title: F-differentiable functions and F-quasianalyticity

Speaker:  Samuel Morley (Nottingham)

Date:  Tuesday, 23rd February 2016

Time:  4pm

Location:  TCD, WR20

Abstract:

Let X be a perfect, compact subset of the complex plane. We usually study those continuous, complex-valued functions f on X such that f has a continuous derivative at all points of X. Unfortunately, the collection of all such functions on X does not have desirable properties as a normed algebra of functions.  In 2003, Bland and Feinstein introduced larger collections of continuous functions on X which have much more desirable properties as normed algebras. They studied those continuous functions on X for which there is an associated continuous function on X which `integrates correctly' along each path in a given collection F of rectifiable paths in X.  We call these functions F-differentiable functions and they have similar properties to the continuous differentiable functions on X. In this talk, we discuss the algebras of F-differentiable functions, their properties, and a notion of quasianalyticity for these algebras.

 

Series: Analysis