## The Mahler basis and other bases. (Base de Mahler et autres.)(French)Zbl 0999.12014

This is an exposition of results of L. Van Hamme [$$p$$-adic functional analysis, Laredo, 1990, 75–88 (1992; Zbl 0773.47039)]. Moreover the author gives the results in a historical context and adds some further results. The aim is to find orthonormal bases for the Banach space of continuous functions from $${\mathbb Z}_p$$ to $$K$$ (a complete nonarchimedean valued field). The norm is the supremum norm.

### MSC:

 12J25 Non-Archimedean valued fields 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:

Mahler basis; orthonormal bases

Zbl 0773.47039