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Asymptotic regularity of Daubechies' scaling functions |
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| Authors: | Ka-Sing Lau Qiyu Sun |
| 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 ; Center for Mathematical Sciences, Zhejiang University, Hangzhou 310027, China |
| 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. |
| Keywords: | Fourier transform scaling function Sobolev exponent wavelet |
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