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CLC number: O174.3
On-line Access: 2024-08-27
Received: 2023-10-17
Revision Accepted: 2024-05-08
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Vector refinement equation and subdivision schemes in Lp spaces
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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",
number="3",
pages="332-338",
year="2002",
publisher="Zhejiang University Press & Springer",
doi="10.1631/jzus.2002.0332"
}
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%A WU Zheng-chang
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%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.2002.0332
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
%@ 1869-1951
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.
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