S. Morley (Nottingham)

will speak on

F-differentiable functions and F-quasianalyticity

Time: 4:00PM
Date: Tue 23rd February 2016
Location: [map]

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 anassociated 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 fort hese algebras.

(This talk is part of the Analysis series.)

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