On wavelets interpolated from a pair of wavelet sets
Ziemowit Rzeszotnik, Darrin M. Speegle · Proceedings of the American Mathematical Society · 2002
We show that any wavelet, with the support of its Fourier transform small enough, can be interpolated from a pair of wavelet sets. In particular, the support of the Fourier transform of such wavelets must contain a wavelet set, answering a special case of an open problem of Larson. The interpolation procedure, which was introduced by X. Dai and D. Larson, allows us also to prove the extension property.