Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
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
MathSciNet review: 687642
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 $.


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


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 43A77

Retrieve articles in all journals with MSC: 43A77


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1983-0687642-3
PII: S 0002-9939(1983)0687642-3
Article copyright: © Copyright 1983 American Mathematical Society