Multiresolution on compact groups
نویسندگان
چکیده
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 [k0Gk 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 in®nite dihedral group, or isomorphically the real orthogonal group in dimension two. Ó 1999 Published by Elsevier Science Inc. All rights reserved. AMS classi®cation: 43A77
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