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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
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 }{\vert _E} \subset {({l^1}(G))^ \wedge }{\vert _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}$.

References [Enhancements On Off] (What's this?)

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