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A class of $M$-dilation scaling functions
with regularity growing proportionally
to filter support width


Authors: Xianliang Shi and Qiyu Sun
Journal: Proc. Amer. Math. Soc. 126 (1998), 3501-3506
MSC (1991): Primary 42C15
DOI: https://doi.org/10.1090/S0002-9939-98-05070-9
MathSciNet review: 1626478
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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper, a class of $M$-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).


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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: https://doi.org/10.1090/S0002-9939-98-05070-9
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
Article copyright: © Copyright 1998 American Mathematical Society