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Proceedings of the American Mathematical Society

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

 

 

$ L\sp{p}$-convolution operators supported by subgroups


Authors: Charles F. Dunkl and Donald E. Ramirez
Journal: Proc. Amer. Math. Soc. 34 (1972), 475-478
MSC: Primary 43A15
DOI: https://doi.org/10.1090/S0002-9939-1972-0296215-9
MathSciNet review: 0296215
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Abstract: Let G be a compact nonabelian group and H be a closed subgroup of G. Then H is a set of spectral synthesis for the Fourier algebra $ A(G)$ (and indeed for $ {A^p}(G),1 \leqq p < \infty $). For $ 1 \leqq p < \infty $, each $ {L^p}(G)$-multiplier T corresponds to a $ {L^p}(H)$-multiplier S by the rule $ (Tf)\vert H = S(f\vert H),f \in A(G)$, if and only if the support of T is contained in H.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0296215-9
Keywords: Fourier algebra, spectral synthesis, $ {L^p}$-multiplier
Article copyright: © Copyright 1972 American Mathematical Society