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
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