## Functions of a $$p$$-adic variable. (Fonctions d’une variable $$p$$-adique.)(English. French summary)Zbl 1223.11144

Berger, Laurent (ed.) et al., Représentations $$p$$-adiques de groupes $$p$$-adiques II: Représentations de $$\text{GL}_2 (\mathbb Q_p)$$ et $$(\varphi, \gamma)$$-modules. Paris: Société Mathématique de France (ISBN 978-2-85629-281-5/pbk). Astérisque 330, 13-59 (2010).
Summary: This text is a compilation of basic results in functional analysis over $$\mathbb Q_p$$. The stress is mainly put on the space of $$\mathcal C^r$$-functions and on its dual of distributions of order $$r$$, the point being that these spaces have come to play an important rôle in $$p$$-adic Langlands theory.
For the entire collection see [Zbl 1192.11001].

### MSC:

 11S80 Other analytic theory (analogues of beta and gamma functions, $$p$$-adic integration, etc.) 46S10 Functional analysis over fields other than $$\mathbb{R}$$ or $$\mathbb{C}$$ or the quaternions; non-Archimedean functional analysis 47S10 Operator theory over fields other than $$\mathbb{R}$$, $$\mathbb{C}$$ or the quaternions; non-Archimedean operator theory
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