Espaces de fonctions de classe C^r sur O_F
Functional Analysis
2012-04-02 v1
Abstract
In this paper we introduce a class of Banach spaces of functions of class C^r (where r is a positive real number) and the associated dual spaces of distributions of order r, which turn out to be useful in p-adic Langlands theory. We construct a Banach basis for these spaces and we give a criterion for telling when a linear form on a space of locally Q_p-polynomial functions extends to a distribution of order r. This generalises the classical results of Amice-V\'elu and Vishik.
Keywords
Cite
@article{arxiv.1203.6766,
title = {Espaces de fonctions de classe C^r sur O_F},
author = {Marco De Ieso},
journal= {arXiv preprint arXiv:1203.6766},
year = {2012}
}
Comments
33 pages, in French. Formerly the first part of arXiv:1111.1016v1