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Proceedings of the American Mathematical Society

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

 

 

Local uncertainty inequalities for compact groups


Authors: John F. Price and Alladi Sitaram
Journal: Proc. Amer. Math. Soc. 103 (1988), 441-447
MSC: Primary 43A30
DOI: https://doi.org/10.1090/S0002-9939-1988-0943063-1
MathSciNet review: 943063
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Abstract: Conditions are established on $ \alpha ,\beta \in {\mathbf{R}}$ for there to exist a constant $ K = K(\alpha ,\beta )$ such that

$\displaystyle \sum\limits_{\gamma \in E} {d(\gamma )\operatorname{tr} (\hat f{{... ...{(\gamma )}^2}} } \right)}^\alpha }{{\left\Vert {{w^\beta }f} \right\Vert}_2}} $

for all $ f \in {L^1}(G)$ and $ E \subseteq \hat G$ where $ G$ is a compact metric group, $ \hat G$ is its dual, $ \hat f$ is the Fourier transform of $ f$ and $ w:G \to {{\mathbf{R}}^ + }$ is the function taking $ x \in G$ to the area of the ball in $ G$ with centre $ e$ and $ x$ on its boundary. This is followed by a partial analogy for compact riemannian manifolds.

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DOI: https://doi.org/10.1090/S0002-9939-1988-0943063-1
Article copyright: © Copyright 1988 American Mathematical Society