Smooth well-localized Parseval wavelets based on simple wavelet sets in Rn
Wavelet set wavelets for scalar dilations in L2(Rn) have had limited applicability for two reasons. The first is that wavelet set wavelets cannot be well-localized. Secondly, the single wavelet sets in dimensions 2 and greater that previously appeared in the literature were complicated unions of infinite collections of convex sets. In this talk, we use generalized filters to smooth new single n-dimensional wavelet sets that are finite unions of convex sets. This process produces single Parseval wavelets for scalar dilations in Rn that are Cr and have Cr Fourier transform, and which have the same multiplicity function as these new simple wavelet sets.