Subspaces with normalized tight frame wavelets in

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 | References | Similar Articles | Additional Information

Abstract: In this paper we investigate the subspaces of which have normalized tight frame wavelets that are defined by set functions on some measurable subsets of 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 that are generated by a Bessel set in a special way. We present some results concerning the relation between a Bessel set and the corresponding subspace of which either has a normalized tight frame wavelet defined by the set function on or is generated by .

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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