On wavelets interpolated from a pair of wavelet sets |
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Authors: | Ziemowit Rzeszotnik Darrin Speegle |
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Institution: | Institute of Mathematics, University of Wroclaw, pl Grunwaldzki 2/4, 50-384 Wroclaw, Poland ; Department of Mathematics & Computer Science, Saint Louis University, St. Louis, Missouri 63103 |
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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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Keywords: | Orthonormal wavelets MSF wavelets interpolated wavelets |
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