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\(p\)-adic continuously differentiable functions of several variables. (English) Zbl 0810.26010

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 \(C^ n(\mathbb{Z}_ p\times \mathbb{Z}_ p\to K)\), the space of \(n\)-times continuously differentiable functions from \(\mathbb{Z}_ p\times \mathbb{Z}_ p\) to \(K\).

MSC:

26E30 Non-Archimedean analysis
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