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Zeitschrift für Analysis und ihre Anwendungen

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Volume 36, Issue 4, 2017, pp. 481–500
DOI: 10.4171/ZAA/1598

Published online: 2017-10-09

Multivariate Wave-Packet Transforms

Arash Ghaani Farashahi[1]

(1) The Johns Hopkins University, Baltimore, USA

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.

Keywords: Multivariate wavelet (Gabor) transforms, multivariate wave-packet representations, multivariate wave-packet groups, multivariate wave-packet transforms

Ghaani Farashahi Arash: Multivariate Wave-Packet Transforms. Z. Anal. Anwend. 36 (2017), 481-500. doi: 10.4171/ZAA/1598