Resumen de P¿adic continuously differentiable functions of several variables

Stany de Smedt

• Let $K$ be a non-Archimedean field containing $\mathbb{Q}_p$, the field of the $p$-adic numbers and let $\mathbb{Z}_p$ denote the ring of $p$-adic integers. In this paper,we construct the Mahler and van der Put base for $C^n(\mathbb{Z}_p\times\mathbb{Z}_p\longrightarrow K)$, the space of $n$-times continuously differentiable functions from $\mathbb{Z}_p\times\mathbb{Z}_p$ to $K$.