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).
@article{urn:eudml:doc:44227,
title = {Orthonormal bases for spaces of continuous and continuously differentiable functions defined on a subset of Zp.},
journal = {Revista Matem\'atica de la Universidad Complutense de Madrid},
volume = {9},
year = {1996},
pages = {295-307},
zbl = {0882.46033},
mrnumber = {MR1430780},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:44227}
}
Verdoodt, Ann. Orthonormal bases for spaces of continuous and continuously differentiable functions defined on a subset of Zp.. Revista Matemática de la Universidad Complutense de Madrid, Tome 9 (1996) pp. 295-307. http://gdmltest.u-ga.fr/item/urn:eudml:doc:44227/