Completeness in the set of wavelets
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- by Gustavo Garrigós and Darrin Speegle PDF
- Proc. Amer. Math. Soc. 128 (2000), 1157-1166 Request permission
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
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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
- Email: gustavo@math.wustl.edu, gustavo@ares.mat.unimi.it
- Darrin Speegle
- Affiliation: Department of Mathematics, Saint Louis University, Saint Louis, Missouri 63103
- Email: speegled@slu.edu
- Received by editor(s): June 15, 1998
- Published electronically: August 17, 1999
- Communicated by: David R. Larson
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 128 (2000), 1157-1166
- MSC (1991): Primary 42C15
- DOI: https://doi.org/10.1090/S0002-9939-99-05198-9
- MathSciNet review: 1646304