February Fourier Talks 2016

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 C^r and have C^r Fourier transform, and which have the same multiplicity function as these new simple wavelet sets.