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Proceedings of the American Mathematical Society

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Subspaces with normalized tight frame wavelets in $\mathbb{R}$


Authors: Xingde Dai, Yuanan Diao and Qing Gu
Journal: Proc. Amer. Math. Soc. 130 (2002), 1661-1667
MSC (1991): Primary 46N99, 46B28
DOI: https://doi.org/10.1090/S0002-9939-01-06257-8
Published electronically: October 23, 2001
MathSciNet review: 1887012
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Abstract: In this paper we investigate the subspaces of $L^2(\mathbb R)$which have normalized tight frame wavelets that are defined by set functions on some measurable subsets of $\mathbb R$ called Bessel sets. We show that a subspace admitting such a normalized tight frame wavelet falls into a class of subspaces called reducing subspaces. We also consider the subspaces of $L^2(\mathbb R)$ that are generated by a Bessel set $E$ in a special way. We present some results concerning the relation between a Bessel set $E$ and the corresponding subspace of $L^2(\mathbb R)$ which either has a normalized tight frame wavelet defined by the set function on $E$ or is generated by $E$.


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Additional Information

Xingde Dai
Affiliation: Department of Mathematics, University of North Carolina at Charlotte, Charlotte, North Carolina 28223-9998

Yuanan Diao
Affiliation: Department of Mathematics, University of North Carolina at Charlotte, Charlotte, North Carolina 28223-9998

Qing Gu
Affiliation: Department of Mathematics, East China Normal University, Shanghai, People’s Republic of China

DOI: https://doi.org/10.1090/S0002-9939-01-06257-8
Received by editor(s): June 26, 2000
Received by editor(s) in revised form: November 21, 2000
Published electronically: October 23, 2001
Communicated by: David R. Larson
Article copyright: © Copyright 2001 American Mathematical Society