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) is the Banach space of continuous functions from Vq to K, equipped with the supremum norm. Our aim is to find normal bases (rn(x)) for C(Vq → K), where rn(x) does not have to be a polynomial.
@article{urn:eudml:doc:41183,
title = {Normal bases for the space of continuous functions defined on a subset of Zp.},
journal = {Publicacions Matem\`atiques},
volume = {38},
year = {1994},
pages = {371-380},
mrnumber = {MR1316633},
zbl = {0840.46056},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41183}
}
Verdoodt, Ann. Normal bases for the space of continuous functions defined on a subset of Zp.. Publicacions Matemàtiques, Tome 38 (1994) pp. 371-380. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41183/