Salma Kuhlmann : Hardy type derivations on generalised series fields.

Posted by , part of the Logic Seminar.

At

Sept. 15, 2009, 4:30 p.m.

In

SEO 612

Abstract

We consider the valued field ${K}:=\mathbb{R}((\Gamma))$ of generalised series (with real coefficients and monomials in a totally ordered multiplicative group $\Gamma\>$). We investigate how to endow ${K}$ with a series derivation, that is a derivation that satisfies some natural properties such as commuting with infinite sums (strong linearity) and (an infinite version of) Leibniz rule. We characterize when such a derivation is of Hardy type, that is, when it behaves like differentiation of germs of real valued functions in a Hardy field. We provide a necessary and sufficent condition for a series derivation of Hardy type to be surjective. (This is joint work with Mickael Matusinski.)

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