Wavelets and Hilbert modules

Details Wavelets and Hilbert modules Wavelets and Hilbert modules

2004-10-03

arxiv.org/abs/math/0410038v1

J. Four. Anal. Appl. 10:6, 573-578, 2004

Mathematics

Functional Analysis

To appear in the Journal of Fourier Analysis and Applications

Scientific paper

A Hilbert module is a generalisation 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 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 modules over the space of essentially bounded functions over higher dimensional tori.

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