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Proceedings of the American Mathematical Society

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Frame wavelet sets in $\mathbb{R}$


Authors: X. Dai, Y. Diao and Q. Gu
Journal: Proc. Amer. Math. Soc. 129 (2001), 2045-2055
MSC (2000): Primary 46N99, 46B28
DOI: https://doi.org/10.1090/S0002-9939-00-05873-1
Published electronically: December 28, 2000
MathSciNet review: 1825916
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Abstract: In this paper, we try to answer an open question raised by Han and Larson, which asks about the characterization of frame wavelet sets. We completely characterize tight frame wavelet sets. We also obtain some necessary conditions and some sufficient conditions for a set $E$ to be a (general) frame wavelet set. Some results are extended to frame wavelet functions that are not defined by frame wavelet set. Several examples are presented and compared with some known results in the literature.


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Additional Information

X. Dai
Affiliation: Department of Mathematics, University of North Carolina at Charlotte, Charlotte, North Carolina 28223
Email: xdai@uncc.edu

Y. Diao
Affiliation: Department of Mathematics, University of North Carolina at Charlotte, Charlotte, North Carolina 28223
Email: ydiao@uncc.edu

Q. Gu
Affiliation: Department of Mathematics, Beijing University, Beijing, People’s Republic of China

DOI: https://doi.org/10.1090/S0002-9939-00-05873-1
Received by editor(s): November 15, 1999
Published electronically: December 28, 2000
Communicated by: David R. Larson
Article copyright: © Copyright 2000 American Mathematical Society