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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


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.

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DOI - 10.1631/jzus.2002.0332

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


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

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[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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