Full paper in PDF:
$%A. Verdoodt, Orthonormal bases for spaces of continuous and continuously differentiable functions defined on a subset of Zp, Rev. Mat. Univ. Complut. Madrid 9 (1996), no. 2, 295307.%$

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