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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Interpolation by transforms of discrete measures


Authors: Louis Pigno and Sadahiro Saeki
Journal: Proc. Amer. Math. Soc. 52 (1975), 156-158
MSC: Primary 43A25
DOI: https://doi.org/10.1090/S0002-9939-1975-0377417-2
MathSciNet review: 0377417
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Abstract: Let $G$ be a compact abelian group, and $\Gamma$ its character group. Given $E \subset \Gamma ,{E^a}$ denotes the set of all accumulation points of $E$ in $\overline \Gamma$, the Bohr compactification of $\Gamma$. In this paper it is shown that the inclusion ${({L^1}(G))^ \wedge }{|_E} \subset {({l^1}(G))^ \wedge }{|_E}$ obtains if and only if $E \cap {E^a} = \emptyset$ and there exists a measure $\mu \epsilon M(G)$ such that $\widehat \mu = 1$ on $E$ and $\widehat \mu = 0$ on $\Gamma \cap {E^a}$.


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Keywords: Compact abelian group, character, Fourier algebra, Bohr compactification, pseudomeasure, set of synthesis
Article copyright: © Copyright 1975 American Mathematical Society