Compactly Supported Refinable Functions with Infinite Masks
نویسندگان
چکیده
A compactly supported scaling function can come from a refinement equation with infinitely many nonzero coefficients (an infinite mask). In this case we prove that the symbol of the mask must have the special rational form ã(Z) = b̃(Z)c̃(Z)/b̃(Z). Any finite combination of the shifts of a refinable function will have such a mask, and will be refinable. We also study compactly supported solutions of vector refinement equations with infinite masks. Our characterization is based on the two-scale similarity transform which plays an essential role in the investigation of multiple wavelets. This concept is used to characterize refinable subspaces of refinable shift-invariant spaces. One advantage of our approach is to provide the refinement masks for generators of refinable subspaces. AMS Subject Classification: Primary 42C15, 41A25, 65F15
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