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ZJUS-A
Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering)  2002, Vol. 3 Issue (3): 332-338    DOI: 10.1631/jzus.2002.0332
Applied Mathematics     
Vector refinement equation and subdivision schemes in Lp spaces
WU Zheng-chang
Department of Mathematics, Zhejiang University, Hangzhou 310027, China
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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.

Key words： Refinement equations      Subdivision schemes      Joint spectral radius     
Received: 21 April 2001     
CLC:  O174.3  
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WU Zheng-chang
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WU Zheng-chang. Vector refinement equation and subdivision schemes in Lp spaces. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2002, 3(3): 332-338.

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http://www.zjujournals.com/xueshu/zjus-a/10.1631/jzus.2002.0332     OR     http://www.zjujournals.com/xueshu/zjus-a/Y2002/V3/I3/332

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[2] ZHOU Jia-li. On the p-norm joint spectral radius[J]. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2003, 4(6): 740-744.