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

Colmez, Pierre

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

Keywords:

\(p\)-adic functional analysis; Amice transform; \(p\)-adic integration