Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

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
DOI: https://doi.org/10.1090/S0002-9939-99-05198-9
Published electronically: August 17, 1999
MathSciNet review: 1646304
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 42C15

Retrieve articles in all journals with MSC (1991): 42C15


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

DOI: https://doi.org/10.1090/S0002-9939-99-05198-9
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