In this paper, we show that for a connected compact Lie group to be acceptable, it is necessary and sufficient its derived subgroup isomorphic direct product of the groups $${\text {SU}}(n)$$ , {Sp}}(n)$$ {SO}}(2n+1)$$ {G}}_2$$ {SO}}(4)$$ . We there are invariant functions on {SO}}_{4}({\mathbb {C}})^{2}$$ which not generated by 1-argument invariants, though {C}})$$ acceptable.

Two Banach algebras are naturally associated with a locally compact group G: the group algebra, L,(G), and the measure algebra, M(G). For these two Banach algebras we determine all isometric involutions. Each of these Banach algebras has a natural involution. We will show that an isometric involution, (*), is the natural involution on £'(<?) if and only if the closure in the strict topology of ...

Given a compact group M, we de®ne the notion of multiresolution of L2…M† with respect to an in®nite sequence of subgroups G0 G1 G2 such that G ˆ [kˆ0Gk is a dense subgroup of M. We give characterizations of various axioms of multiresolution, demonstrate the existence and give the construction of a wavelet basis for L2…M†. We also construct stationary multiresolution and wavelets from cyclic vec...

These notes are a gloss on the first chapter of Walter Rudin’s Fourier Analysis on Groups, and may be helpful to someone reading Rudin. The results I do prove are proved in more detail than they are in Rudin. I caution that before reading the first chapter of that book it is know about the Gelfand transform on commutative Banach algebras because results from that are used without even stating t...