Simple Wavelet Sets for Scalar Dilations in ℝ2
Wavelet sets for dilation by any scalar d > 1 in L2(ℝ2) are constructed that are finite unions of convex polygons. Such simple wavelet sets for dilation by 2 were widely conjectured to be impossible. The examples are built using the generalized scaling set technique of Baggett et al. . Generalizations to other expansive dilations in L2(ℝ2) are discussed.
KeywordsMultiresolution Analysis Tight Frame Construction Technique Consistency Equation Scalar Dilation
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