Multivariate Wave-Packet Transforms

Abstract

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