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Received: 2001-04-21

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Journal of Zhejiang University SCIENCE A 2002 Vol.3 No.3 P.332-338

http://doi.org/10.1631/jzus.2002.0332


Vector refinement equation and subdivision schemes in Lp spaces


Author(s):  WU Zheng-chang

Affiliation(s):  Department of Mathematics, Zhejiang University, Hangzhou 310027, China

Corresponding email(s):   wuzhengchang@HZCNC.com

Key Words:  Refinement equations, Subdivision schemes, Joint spectral radius


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WU Zheng-chang. Vector refinement equation and subdivision schemes in Lp spaces[J]. Journal of Zhejiang University Science A, 2002, 3(3): 332-338.

@article{title="Vector refinement equation and subdivision schemes in Lp spaces",
author="WU Zheng-chang",
journal="Journal of Zhejiang University Science A",
volume="3",
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pages="332-338",
year="2002",
publisher="Zhejiang University Press & Springer",
doi="10.1631/jzus.2002.0332"
}

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TY - JOUR
T1 - Vector refinement equation and subdivision schemes in Lp spaces
A1 - WU Zheng-chang
J0 - Journal of Zhejiang University Science A
VL - 3
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SP - 332
EP - 338
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Y1 - 2002
PB - Zhejiang University Press & Springer
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DOI - 10.1631/jzus.2002.0332


Abstract: 
In this paper we will first prove that the nontrivial Lp solutions of the vector refinement equation exist if and only if the corresponding subdivision scheme with a suitable initial function converges in Lp without assumption of the stability of the solutions. Then we obtain a characterization of the convergence of the subdivision scheme in terms of the mask. This gives a complete answer to the existence of Lp solutions of the refinement equation and the convergence of the corresponding subdivision schemes.

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article

Reference

[1] Ben-Artzi,A., Ron,A.,1990. On the integer translates of a compactly supported function: dual bases and linear projectors. SIAM J. Math. Anal.,21: 1550-1562.

[2] Cavaretta,A.S.,Dahmen,W., Micchelli,C.A., 1991. Stationary subdivision. Memoirs of Amer.Math. Soc., 93

[3] Han, B., Jia,R.Q., 1998. Multivariate refinement equations and convergence of subdivision schemes. SIAM J. Math. Anal., 29: 1177-1199.

[4] Heil,C., Collela,D., 1996. Matrix refinement equations, existence and uniqueness. J. Fourier Anal. Appl., 2: 363-377.

[5] Jia,R.Q., 1995. Subdivision schemes in Lp spaces. Advances in computation mathematics, 3:309-341.

[6] Jia,R.Q., 1997. Shift-invariant spaces on the real line. Proc. Amer. Math. Soc., 125:785-793.

[7] Jia,R.Q.,Riemenschneider,S.D., Zhou,D.X., 1998. Vector subdivision schemes and multiple wavelets. Mathematics of computation,67:1533-1563

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