Abstract:We study the phenomenon that regularly spaced subsequences of the control points in subdivision may converge to scalar multiples of the same limit function, even though subdivision itself is divergent. We present different sets of easily checkable sufficient conditions for this phenomenon (which we term subsequence convergence) to occur, study the basic properties of subsequence convergence, show how certain results from subdivision carry over to this case, show an application for decorative effects, and use our results to build nested sets of refinement masks, which provide some insight into the structure of the set of refinable functions. All our results are formulated for a general integer dilation factor.
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- Deter de Wet
- Affiliation: Department of Mathematical Sciences, Mathematics Division, Private Bag X1, Matieland 7602, South Africa
- Received by editor(s): April 16, 2008
- Received by editor(s) in revised form: April 29, 2009
- Published electronically: October 18, 2010
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
- Journal: Math. Comp. 80 (2011), 973-994
- MSC (2010): Primary 65D10, 65D17, 41A99
- DOI: https://doi.org/10.1090/S0025-5718-2010-02380-4
- MathSciNet review: 2772104