Espaces de fonctions de classe C^r sur O_F

Details Espaces de fonctions de classe C^r sur O_F Espaces de fonctions de classe C^r sur O_F

2012-03-30

arxiv.org/abs/1203.6766v1

Mathematics

Functional Analysis

33 pages, in French. Formerly the first part of arXiv:1111.1016v1

Scientific paper

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.

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