Multiresolution on compact groups Original Research Article

Given a compact group M, we define the notion of multiresolution of L2(M) with respect to an infinite sequence of subgroups G0subset of or equal toG1subset of or equal toG2subset of or equal tocdots, three dots, centered such that G=union or logical sum∞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.