Multivariate Wave-Packet Transforms

This paper presents a study for square-integrability of classical multivariate wave-packets in L2(Rd)L2(Rd) via group representation theory. The abstract notions of multivariate wave-packet groups and multivariate wave-packet representations will be introduced and as the main result, we prove an admissibility condition on closed subgroups of GL(d,R)(d,R), which guarantees the square integrability of classical multivariate wave-packet representations on L2(Rd)L2(Rd). Finally, we present application of our results in the case of different admissible subgroups.