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On the closed subfields of [...] Q ¯   p Q ¯ ˜ p

Sever Achimescu, Victor Alexandru, Corneliu Stelian Andronescu (2016)

Open Mathematics

Let p be a prime number, and let [...] Q¯ p Q ¯ ˜ 𝐩 be the completion of Q with respect to the pseudovaluation w which extends the p-adic valuation vp. In this paper our goal is to give a characterization of closed subfields of [...] Q¯ p Q ¯ ˜ 𝐩 , the completion of Q with respect w, i.e. the spectral extension of the p-adic valuation vp on Q.

Orthonormal bases for spaces of continuous and continuously differentiable functions defined on a subset of Zp.

Ann Verdoodt (1996)

Revista Matemática de la Universidad Complutense de Madrid

Let K be a non-Archimedean valued field which contains Qp, and suppose that K is complete for the valuation |·|, which extends the p-adic valuation. Vq is the closure of the set {aqn | n = 0,1,2,...} where a and q are two units of Zp, q not a root of unity. C(Vq --> K) (resp. C1(Vq --> K)) is the Banach space of continuous functions (resp. continuously differentiable functions) from Vq to K. Our aim is to find orthonormal bases for C(Vq --> K) and C1(Vq --> K).

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