Abstract
It is proved that associated with every wavelet set is a closely related “regularized” wavelet set which has very nice properties. Then it is shown that for many (and perhaps all) pairs E, F, of wavelet sets, the corresponding MSF wavelets can be connected by a continuous path in L2(ℝ) of MSF wavelets for which the Fourier transform has support contained in E ∪ F. Our technique applies, in particular, to the Shannon and Journe wavelet sets.
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Communicated by Guido Weiss
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Ionascu, E.J., Larson, D.R. & Pearcy, C.M. On wavelet sets. The Journal of Fourier Analysis and Applications 4, 711–721 (1998). https://doi.org/10.1007/BF02479674
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DOI: https://doi.org/10.1007/BF02479674