Multivariate Wave-Packet Transforms

This paper presents a study for square-integrability of classical multivariate wave-packets in L-2 (R-d) 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), which guarantees the square integrability of classical multivariate wave-packet representations on L-2 (R-d). Finally, we present application of our results in the case of different admissible subgroups.