Asymptotic regularity

of Daubechies' scaling functions

Authors:
Ka-Sing Lau and Qiyu Sun

Journal:
Proc. Amer. Math. Soc. **128** (2000), 1087-1095

MSC (1991):
Primary 42C15, 26A15, 26A18, 39A10, 42A05

DOI:
https://doi.org/10.1090/S0002-9939-99-05251-X

Published electronically:
July 28, 1999

MathSciNet review:
1654093

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Let , , be Daubechies' scaling function with symbol , and let , be the corresponding Sobolev exponent. In this paper, we make a sharp estimation of , and we prove that there exists a constant independent of such that

This answers a question of Cohen and Daubeschies (* Rev. Mat. Iberoamericana*, 12(1996), 527-591) positively.

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Additional Information

**Ka-Sing Lau**

Affiliation:
Department of Mathematics, University of Pittsburgh, Pittsburgh, Pennsylvania 15260;
Institute of Mathematical Sciences, The Chinese University of Hong Kong, Shatin, Hong Kong

**Qiyu Sun**

Affiliation:
Center for Mthematical Sciences, Zhejiang University, Hangzhou 310027, China

Address at time of publication:
Department of Mathematics, National University of Singapore, 10 Kent Ridge Crescent, Singapore

Email:
matsunqy@leonis.nus.edu.sg

DOI:
https://doi.org/10.1090/S0002-9939-99-05251-X

Keywords:
Fourier transform,
scaling function,
Sobolev exponent,
wavelet

Received by editor(s):
November 3, 1997

Received by editor(s) in revised form:
May 30, 1998

Published electronically:
July 28, 1999

Communicated by:
David R. Larson

Article copyright:
© Copyright 2000
American Mathematical Society