Higher Rank Wavelets

Olphert, Sean and Power, Stephen (2011) Higher Rank Wavelets. Canadian Journal of Mathematics, 63. pp. 689-720. ISSN 0008-414X

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Abstract

A theory of higher rank multiresolution analysis is given in the setting of abelian multiscalings. This theory enables the construction, from a higher rank MRA, of finite wavelet sets whose multidilations have translates forming an orthonormal basis in . While tensor products of uniscaled MRAs provide simple examples we construct many nonseparable higher rank wavelets. In particular we construct \emph{Latin square wavelets} as rank 2 variants of Haar wavelets. Also we construct nonseparable scaling functions for rank 2 variants of Meyer wavelet scaling functions, and we construct the associated nonseparable wavelets with compactly supported Fourier transforms. On the other hand we show that compactly supported scaling functions for biscaled MRAs are necessarily separable.

Item Type:
Journal Article
Journal or Publication Title:
Canadian Journal of Mathematics
Uncontrolled Keywords:
/dk/atira/pure/researchoutput/libraryofcongress/qa
Subjects:
ID Code:
59562
Deposited By:
Deposited On:
26 Oct 2012 15:32
Refereed?:
Yes
Published?:
Published
Last Modified:
01 Jan 2020 08:12