Abstract
Let ( G, K) be a Riemannian symmetric pair of the compact type and let V × K be the associated Cartan motion group. We establish a body of approximation theorems that permit the transfer of Fourier analysis from the group G to the Cartan motion group. As a consequence, we prove an analogue of a theorem of de Leeuw concerning restriction of Fourier multipliers of the group R to the group Z . The latter theorem extends an earlier result of R. L. Rubin for the case where G = SO(3), K = SO(2), and V × K is the Euclidean motion group.
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