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Proceedings of the American Mathematical Society

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

 

 

Bounded projections on Fourier-Stieltjes transforms


Authors: Charles F. Dunkl and Donald E. Ramirez
Journal: Proc. Amer. Math. Soc. 31 (1972), 122-126
MathSciNet review: 0288520
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Abstract: We study certain algebraic projections on the measure algebra (of a locally compact abelian group) which extend to bounded projections on the uniform closure of the Fourier-Stieltjes transforms. These projections arise by studying a Raikov system of subsets induced by locally compact subgroups. These results generalize the inequality $ \vert\vert{\hat \mu _d}\vert{\vert _\infty } \leqq \vert\vert\hat \mu \vert{\vert _\infty }$ (where $ \mu $ is in the measure algebra, $ {\mu _d}$ is the discrete part of $ \mu $, and $ \vert\vert\hat \mu \vert{\vert _\infty }$ is the sup-norm of the Fourier-Stieltjes transform).


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DOI: https://doi.org/10.1090/S0002-9939-1972-0288520-7
Keywords: Measure algebra of a locally compact abelian group, Fourier-Stieltjes transform, Raikov system of subsets, positive definite function
Article copyright: © Copyright 1972 American Mathematical Society