✦ LIBER ✦

Multiplicative Zak Transform

✍ Scribed by I. Gertner; R. Tolimieri

Publisher: Elsevier Science
Year: 1995
Tongue: English
Weight: 260 KB
Volume: 6
Category: Article
ISSN: 1047-3203
DOI: 10.1006/jvci.1995.1008

No coin nor oath required. For personal study only.

✦ Synopsis

A multiplicative Zak transform will be defined on the space (L^{2}(0, \infty)) which can be used to study properties of finite bandwidth affine group wavelet systems of the type considered in "Painless Nonorthogonal Expansions" by I. Daubechies, A. Grossman, and Y. Meyer (J. Math. Phys. 27(5), 1986, 1271-1283). The multiplicatice Zak transform can be viewed as the multiplicative analogue of the standard Zak transform and both are special instances of intertwining operators for irreducible representations of Heisenberg group over locally compact abelian groups. Fundamental formulas involving products of multiplicative Zak transforms will be derived and applied to establishing frame conditions for finite bandwidth affine group wavelet systems. 1995 Academic Press, Inc.

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