On wavelets interpolated from a pair of wavelet sets

Rzeszotnik, Ziemowit; Speegle, Darrin

doi:10.1090/S0002-9939-02-06416-X

On wavelets interpolated from a pair of wavelet sets
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by Ziemowit Rzeszotnik and Darrin Speegle PDF

Proc. Amer. Math. Soc. 130 (2002), 2921-2930 Request permission

Abstract:

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.

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