AN EQUIVALENCE RELATION ON WAVELETS IN HIGHER DIMENSIONS
Biswaranjan Behera · Bulletin of the London Mathematical Society · 2004
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 L2(Rn) 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. 2000 Mathematics Subject Classification 42C40 (primary); 47A15 (secondary).