Multivariate Wave-Packet Transforms

  • Arash Ghaani Farashahi

    The Johns Hopkins University, Baltimore, USA


This paper presents a study for square-integrability of classical multivariate wave-packets in L2(Rd)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,R)(d, \mathbb R), which guarantees the square integrability of classical multivariate wave-packet representations on L2(Rd)L^2({\mathbb{R}^d}). Finally, we present application of our results in the case of different admissible subgroups.

Cite this article

Arash Ghaani Farashahi, Multivariate Wave-Packet Transforms. Z. Anal. Anwend. 36 (2017), no. 4, pp. 481–500

DOI 10.4171/ZAA/1598