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AN EQUIVALENCE RELATION ON WAVELETS IN HIGHER DIMENSIONS

Published online by Cambridge University Press:  02 February 2004

BISWARANJAN BEHERA
BISWARANJAN BEHERA
Affiliation:
Statistics and Mathematics Unit, Indian Statistical Institute, 203, B. T. Road, Calcutta 700108, Indiabr_behera@yahoo.com
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Abstract

The action of translation operators on wavelet subspaces in higher dimensions is investigated. This action defines an equivalence relation on the set of single wavelets of $L^2(\mathbb R^n)$ associated with an arbitrary dilation matrix. The corresponding equivalence classes are characterized in terms of the support of the Fourier transform of the wavelets. Further, examples of wavelets in each of these classes are constructed. This construction shows the existence of wavelets for which the associated wavelet subspaces are invariant under various groups of translation operators.

Keywords

42C40 (primary)47A15 (secondary)
Type
Papers
Information
Bulletin of the London Mathematical Society , Volume 36 , Issue 2 , March 2004 , pp. 221 - 230
Copyright
© The London Mathematical Society 2004

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