Journal of Fourier Analysis and Applications

, Volume 10, Issue 6, pp 573–598 | Cite as

Wavelets and Hilbert Modules

Article

Abstract

A Hilbert C*-module is a generalization of a Hilbert space for which the inner product takes its values in a C*-algebra instead of the complex numbers. We use the bracket product to construct some Hilbert C*-modules over a group C*-algebra which is generated by the group of translations associated with a wavelet. We shall investigate bracket products and their Fourier transform in the space of square integrable functions in Euclidean space. We will also show that some wavelets are associated with Hilbert C*-modules over the space of essentially bounded functions over higher dimensional tori.

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Copyright information

© Birkhauser Boston 2004

Authors and Affiliations

  1. 1.School of Informatics and Engineering, Flinders University of South Australia, GPO Box 2100, Adelaide, SA, 5001Australia

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