|
Journal of Zhejiang University SCIENCE A
ISSN 1673-565X(Print), 1862-1775(Online), Monthly
2002 Vol.3 No.3 P.332-338
Vector refinement equation and subdivision schemes in Lp spaces
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
References:
Open peer comments: Debate/Discuss/Question/Opinion
<1>
DOI:
10.1631/jzus.2002.0332
CLC number:
O174.3
Download Full Text:
Downloaded:
2382
Clicked:
4288
Cited:
0
On-line Access:
Received:
2001-04-21
Revision Accepted:
2001-06-06
Crosschecked: