Normal bases for the space of continuous functions defined on a subset of $\Bbb Z_p$

Autores: Ann Verdoodt
Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 38, Nº 2, 1994, págs. 371-380
Idioma: inglés
DOI: 10.5565/publmat_38294_07
Títulos paralelos:
- Bases normales para el espacio de las funciones continuas definidas sobre un subconjunto de Zp
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Resumen
- Let $K$ be a non-archimedean valued field which contains $\Bbb Q_p$ and suppose that $K$ is complete for the valuation $|\cdot|$, which extends the $p$-adic valuation. $V_q$ is the closure of the set $\{aq^n|n=0,1,2,\dots\}$ where $a$ and $q$ are two units of $\Bbb Z_p$, $q$ not a root of unity. $C(V_q\rightarrow K)$ is the Banach space of continuous functions from $V_q$ to $K$, equipped with the supremum norm. Our aim is to find normal bases $(r_n(x))$ for $C(V_q\rightarrow K)$, where $r_n(x)$ does not have to be a polynomial.