Normes de Sobolev et convoluteurs bornés sur \(L^ 2(G)\). (Sobolev norms and bounded convolvers on \(L^ 2(G)\)) (Q810809)

A locally compact group G equipped with a length-function L has property (RD) with respect to L if any rapidly decreasing function on G defines a bounded convolver on \(L^ 2(G)\). We give a fairly general sufficient condition for the pair (G,L) to have property (RD). For such a pair, we characterize positive definite functions on G that are weakly associated to the left regular representation and, in the discrete case, we deal with approximation properties of the Fourier algebra of G.