RMC - Vol. 9, Num. 2 - Ann Verdoodt

Full paper in PDF:
$%A. Verdoodt, Orthonormal bases for spaces of continuous and continuously differentiable functions defined on a subset of Z_p, Rev. Mat. Univ. Complut. Madrid 9 (1996), no. 2, 295–307.%$

Orthonormal Bases for Spaces of Continuous and Continuously Differentiable Functions Defined on a Subset of Z_p

Ann VERDOODT

Vrije Universiteit Brussel
Faculty of Applied Sciences
Pleinlaan 2
B-1050 Brussels — Belgium

Received: Frebuary 6, 1995

ABSTRACT

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 $n {aq |n= 0,1,2,...}$ where $a$ and $q$ are two units of $Z p$ , $q$ not a root of unity. $C(V -- > K) q$ (resp. $C (V -- > K) 1 q$ ) 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 $C1(Vq-- > K)$ .

1991 Mathematics Subject Classification: 46S10.