Wandering r-tuples for unitary systems

The properties of the set Wr(U) of all complete wandering r-tuples for a system U of unitary operators acting on a Hilbert space are investigated by parameterizing Wr(U) in terms of a fixed wandering r-tuple Ψ and the set of all unitary operators which locally commute with U at Ψ. The special case of greatest interest is the system 〈D,T〉 of dilation (by 2) and translation (by 1) unitary operators acting on L2(R), for which the complete wandering r-tuples are precisely the orthogonal multiwavelets with multiplicity r. We also give some examples for its application.