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# $L^p$-Convolution Operators Supported by Subgroups

Charles F. Dunkl and Donald E. Ramirez
Proceedings of the American Mathematical Society
Vol. 34, No. 2 (Aug., 1972), pp. 475-478
DOI: 10.2307/2038393
Stable URL: http://www.jstor.org/stable/2038393
Page Count: 4
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 $(Tf)|H = S(f|H), f \in A(G)$, if and only if the support of $T$ is contained in $H$.