Hardy type derivations on generalised series fields

JOURNAL OF ALGEBRA

卷:351

Article

Kuhlmann, Salma¹  Matusinski, Mickael¹ 

[1] Univ Konstanz, Fachbereich Math & Stat, D-78457 Constance, Germany

关键词: Generalised series fields;    Hardy fields;    Derivations;    Valuation theory;    Asymptotic integration;   

DOI  :  10.1016/j.jalgebra.2011.11.024

来源: Elsevier

【 摘 要 】

We consider the valued field K := 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 characterise 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 sufficient condition for a series derivation of Hardy type to be surjective. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free