De Smedt, Stany \(p\)-adic continuously differentiable functions of several variables. (English) Zbl 0810.26010 Collect. Math. 45, No. 2, 137-152 (1994). 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 \(K\). Reviewer: S.De Smedt (Brussel) Cited in 4 Documents MSC: 26E30 Non-Archimedean analysis Keywords:\(C^ n\)-functions; orthonormal bases; \(p\)-adic analysis; non-Archimedean field; van der Put base; Mahler base PDFBibTeX XMLCite \textit{S. De Smedt}, Collect. Math. 45, No. 2, 137--152 (1994; Zbl 0810.26010) Full Text: EuDML