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Frame wavelet sets in 
Author(s):
X.
Dai;
Y.
Diao;
Q.
Gu
Journal:
Proc. Amer. Math. Soc.
129
(2001),
2045-2055.
MSC (2000):
Primary 46N99, 46B28
Posted:
December 28, 2000
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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  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.
References:
-
- 1.
- L. Baggett, H. Medina and K. Merrill, Generalized Multiresolution Analyses, and a Construction Procedure for All Wavelet Sets in
 preprint. - 2.
- X. Dai, Y. Diao and Q. Gu, Normalized Tight Frame Wavelet Sets, preprint.
- 3.
- I. Daubechies, The wavelet transform, time-frequency localization and signal analysis, IEEE Trans. Inform. Theory, 36, (1990), 961-1005. MR 91e:42038
- 4.
- I. Daubechies, Ten Lectures on Wavelets, CBS-NSF Regional Conferences in Applied Mathematics, 61, SIAM, (1992). MR 93e:42045
- 5.
- I. Daubechies, A. Grossman, Y. Meyer, Painless nonorthogonal expansions, J. Math. Phys., 27(5), (1986), 1271-1283. MR 87e:81089
- 6.
- R. J. Duffin, A. C. Shaffer, A class of nonharmonic Fourier Series, Trans. Amer. Math. Soc., 72, (1952), 341-366. MR 13:839a
- 7.
- D. Han and D. Larson, Bases, Frames and Group representations, Memoirs, AMS, to appear.
- 8.
- E. Hernández, G. Weiss, A first course on wavelets, CRC Press, Boca Raton, (1996). MR 97i:42015
- 9.
- S. Mallat, Multiresolution approximations and wavelet orthonormal basis of
 Trans. Amer. Math. Soc., 315, (1989) 69-87. MR 90e:42046 - 10.
- Y. Meyer, Ondelettes et operateurs I, Hermann editeurs des sciences et des arts, 1990; Eng. transl, Wavelets and Operators, Camb. Studies in Adv. Math., 37, 1992. MR 93i:42002
- 11.
- Y. Meyer, Wavelets: Algorithms and Applications, transl. from Fr., SIAM, Philadelphia, 1993. MR 95f:94005
- 12.
- B. Sz-Nagy, Expansion theorems of Paley-Wiener type, Duke Math. J., 14, (1947), 975-978.
- 13.
- R. M. Young, An introduction to nonharmonic Fourier series, Academic Press, New York, (1980). MR 81m:42027
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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:
10.1090/S0002-9939-00-05873-1
PII:
S 0002-9939(00)05873-1
Received by editor(s):
November 15, 1999
Posted:
December 28, 2000
Communicated by:
David R. Larson
Copyright of article:
Copyright
2000,
American Mathematical Society
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