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On wavelets interpolated from a pair of wavelet sets

Authors: Ziemowit Rzeszotnik and Darrin Speegle
Journal: Proc. Amer. Math. Soc. 130 (2002), 2921-2930
MSC (2000): Primary 42C40
Published electronically: May 8, 2002
MathSciNet review: 1908915
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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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Additional Information

Ziemowit Rzeszotnik
Affiliation: Institute of Mathematics, University of Wroclaw, pl Grunwaldzki 2/4, 50-384 Wroclaw, Poland

Darrin Speegle
Affiliation: Department of Mathematics & Computer Science, Saint Louis University, St. Louis, Missouri 63103

Keywords: Orthonormal wavelets, MSF wavelets, interpolated wavelets
Received by editor(s): September 19, 2000
Received by editor(s) in revised form: March 22, 2001
Published electronically: May 8, 2002
Communicated by: David R. Larson
Article copyright: © Copyright 2002 American Mathematical Society