Multiresolution on compact groups

Given a compact group M, we define the notion of multiresolution of L-2(M) with respect to an infinite sequence of subgroups G(0) subset of or equal t o G(1) subset of or equal to G(2) subset of or equal to ... such that G = b oolean ORk=0infinity G(k) is a dense subgroup of M. We give characterizatio ns of various axioms of multiresolution, demonstrate the existence and give the construction of a wavelet basis for L-2(M). We also construct stationa ry multiresolution and wavelets from cyclic vectors. An example of multires olution on a non-abelian compact group is given for the infinite dihedral g roup, or isomorphically the real orthogonal group in dimension two. (C) 199 9 Published by Elsevier Science Inc. All rights reserved.