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A class of  -dilation scaling functions with regularity growing proportionally to filter support width
Author(s):
Xianliang
Shi;
Qiyu
Sun
Journal:
Proc. Amer. Math. Soc.
126
(1998),
3501-3506.
MSC (1991):
Primary 42C15
MathSciNet review:
1626478
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Abstract:
In this paper, a class of  -dilation scaling functions with regularity growing proportionally to filter support width is constructed. This answers a question proposed by Daubechies on p.338 of her book Ten Lectures on Wavelets (1992).
References:
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- N. Bi, X. Dai and Q. Sun, Construction of compactly supported
 -band wavelets, Appl. Comput. Harmonic Anal., To appear. - [D]
- I. Daubechies, Ten Lectures on Wavelets, CBMS-NSF Regional Conference Series in Applied Mathematics 61, Philadephia, 1992. MR 93e:42045
- [DL]
- I. Daubechies and J. Lagarias, Two-scale difference equation I: existence and global regularity of solution, SIAM J. Math. Anal., 22(1991), 1388-1410. MR 92d:39001
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- P. N. Heller, Rank wavelets with
 vanishing moments, SIAM J. Matrix Anal. Appl., 16(1995), 502-519. MR 95k:42058 - [HW1]
- P. N. Heller and R. O. Wells, Jr., The spectral theory of multiresolution operators and applications, In Wavelets: Theory, Algorithms, and Applications, edited by C. K. Chui, L. Montefusco, and L. Puccio, Academic Press, 1994, pp. 13-42. MR 96a:42046
- [HW2]
- P. N. Heller ad R. O. Wells Jr., Sobolev regularity for rank wavelets, CML Technical Report TR 96-08, Computational Mathematics Laboratory, Rice University, 1996.
- [HSZ]
- D. Huang, Q. Sun and Z. Zhang, Integral representation of -band filter of Daubechies type, Chinese Sciences Bulletin, 42(1997), 803-807. CMP 97:17
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- Y. Meyer, Ondelettes et Opérateurs,I: Ondelettes, Hermann, Paris, 1990. MR 93i:42002
- [So]
- P. M. Soardi, Hölder regularity of compactly supported
 -wavelets, Constr. Approx., To appear. - [S]
- Q. Sun, Sobolev exponent estimates and asymptotic regularity of band Daubechies' scaling functions, Preprint, 1997.
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Additional Information:
Xianliang
Shi
Affiliation:
Department of Mathematics, Texas A&M University, College Station, Texas 77843-3368
Email:
xshi@math.tamu.edu
Qiyu
Sun
Affiliation:
Center for Mathematical Sciences, Zhejiang University, Hangzhou, Zhejiang 310027, People's Republic of China
Address at time of publication:
Department of Mathematics, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260, Singapore
Email:
matsunqy@leonis.nus.edu.sg
DOI:
10.1090/S0002-9939-98-05070-9
PII:
S 0002-9939(98)05070-9
Received by editor(s):
November 20, 1995
Additional Notes:
The first author is supported by the Texas Higher Education Coordinating Board under Grant Number 999903-109. The second author is partially supported by the National Natural Sciences Foundation of China # 69735020, the Tian Yuan Foundation, the Doctoral Bases Promotion Foundation of National Educational Commission of China # 97033519 and the Zhejiang Provincial Sciences Foundation of China # 196083, and by the Wavelets Strategic Research Program, National University of Singapore, under a grant from the National Science and Technology Board and the Ministry of Education, Singapore.
Communicated by:
J. Marshall Ash
Copyright of article:
Copyright
1998,
American Mathematical Society
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