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Proceedings of the American Mathematical Society

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

 

 

Fourier coefficients of continuous functions on compact groups


Author: Barbara Heiman
Journal: Proc. Amer. Math. Soc. 87 (1983), 685-690
MSC: Primary 43A77
DOI: https://doi.org/10.1090/S0002-9939-1983-0687642-3
MathSciNet review: 687642
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Abstract: Let $ G$ be an infinite compact group with dual object $ \Sigma $. Letting $ {\mathcal{K}_\sigma }$ be the representation space for $ \sigma \in \Sigma $, $ {\mathcal{E}^2}(\Sigma )$ is the set $ \{ A = ({A^\sigma }) \in \Pi \mathcal{B}({\mathcal{K}_\sigma }):\left\Vert A \... ... _\sigma }{d_\sigma }\operatorname{Tr} ({A^\sigma }{A^{\sigma *}}) < \infty \} $. For $ A \in {\mathcal{E}^2}(\Sigma )$, we show that there is a function $ f$ in $ C(G)$ such that $ {\left\Vert f \right\Vert _\infty } \leqslant C{\left\Vert A \right\Vert _2}$ and $ \operatorname{Tr} (\hat f(\sigma )\hat f{(\sigma )^*}) \geqslant \operatorname{Tr} ({A^\sigma }{A^{\sigma *}})$ for every $ \sigma \in \Sigma $.


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DOI: https://doi.org/10.1090/S0002-9939-1983-0687642-3
Article copyright: © Copyright 1983 American Mathematical Society