Multiresolution on compact groups

AbstractGiven a compact group M, we define the notion of multiresolution of L2(M) with respect to an infinite sequence of subgroups G0⊆G1⊆G2⊆⋯ such that G=∪∞k=0Gk 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 vectors. An example of multiresolution on a non-abelian compact group is given for the infinite dihedral group, or isomorphically the real orthogonal group in dimension two