Full paper in PDF:
$%A. Verdoodt, Orthonormal bases for spaces of continuous and continuously
differentiable
functions defined on a subset of Zp, Rev. Mat. Univ. Complut. Madrid 9 (1996), no. 2,
295–307.%$
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
be a non-Archimedean valued field which contains
, and suppose that
is complete for the valuation
, which extends the
-adic valuation.
is the closure of the set
where
and
are two units
of
,
not a root of unity.
(resp. ) is the Banach
space of continuous functions (resp. continuously differentiable functions) from
to
. Our aim is to find orthonormal bases for
and
.
1991 Mathematics Subject Classification: 46S10.