IJPAM: Volume 88, No. 1 (2013)
WALSH-FOURIER COEFFICIENTS OF LINEAR MAPPINGS
Miloslav Duchoň
Mathematical Institute
Slovak Academy of Sciences
Štefánikova 49, SK-814 73 Bratislava, SLOVAKIA
Mathematical Institute
Slovak Academy of Sciences
Štefánikova 49, SK-814 73 Bratislava, SLOVAKIA
Abstract. Let be a sequence of elements of a locally convex space
. Let
be a homogeneous Banach space on the Cantor group
. In this paper the necessary and sufficient conditions are given for
to be the Walsh-Fourier coefficients of some continuous, weakly compact or compact linear mapping
.
(As for Cantor group and related facts, see R.E. Edwards, Fourier Series, at the end of the paper.)
Received: July 19, 2013
AMS Subject Classification: 28E10, 81P10
Key Words and Phrases: locally convex space, weakly compact semivariation, vector measure on Borel subsets
Download paper from here.
DOI: 10.12732/ijpam.v88i1.8 How to cite this paper?
Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2013
Volume: 88
Issue: 1