Some Remarks concerning Functions with All Their Wavelet Coefficients Vanishing
نویسنده
چکیده
For a compactly supported wavelet there are non-polynomial functions with all their wavelet coeecients vanishing, and the class U of such functions has been characterized by P.-G. Lemari e-Rieusset. In this paper we study the properties of this class U more closely, and show how U relates to the characterization of function spaces in terms of wavelet coeecients, the asymptotic behavior of the wavelet and the scaling function at dyadic rationals, and the renormalization of homogeneous wavelet expansions. We also show that essentially the same characterization holds in the multivariate case, though the description is then less explicit.
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