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Completeness in the set of wavelets

Authors: Gustavo Garrigós and Darrin Speegle
Journal: Proc. Amer. Math. Soc. 128 (2000), 1157-1166
MSC (1991): Primary 42C15
Published electronically: August 17, 1999
MathSciNet review: 1646304
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Abstract: We study the completeness properties of the set of wavelets in $L^{2}(\mathbb{R})$. It is well-known that this set is not closed in the unit ball of $L^{2}(\mathbb{R})$. However, if one considers the metric inherited as a subspace (in the Fourier transform side) of $L^{2}(\mathbb{R},d\xi ) \cap L^{2}(\mathbb{R}_{*},{\frac{{d\xi }}{{|\xi |}}})$, we do obtain a complete metric space.

References [Enhancements On Off] (What's this?)

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Additional Information

Gustavo Garrigós
Affiliation: Department of Mathematics, Washington University, Saint Louis, Missouri 63130
Address at time of publication: Dipartimento di Matematica, Università di Milano, Via C. Saldini, 50, 20133, Milano, Italy

Darrin Speegle
Affiliation: Department of Mathematics, Saint Louis University, Saint Louis, Missouri 63103

Keywords: Wavelets, completeness, equivalent metrics
Received by editor(s): June 15, 1998
Published electronically: August 17, 1999
Communicated by: David R. Larson
Article copyright: © Copyright 2000 American Mathematical Society

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