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


Abstract. Let $(x_n)$ be a sequence of elements of a locally convex space $X$. Let $H(\mathcal C)$ be a homogeneous Banach space on the Cantor group $\mathcal C$. In this paper the necessary and sufficient conditions are given for $(x_n)$ to be the Walsh-Fourier coefficients of some continuous, weakly compact or compact linear mapping $u:H(\mathcal C)\to X$.

(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

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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