文献类型：期刊文献

英文题名：Invariance property of proximity conditions in nonlinear subdivision

作者：Xie, Gang[1];Yu, Thomas P. Y.[2]

机构：[1]E China Univ Sci & Technol, Dept Math, Shanghai 200237, Peoples R China;[2]Drexel Univ, Dept Math, Philadelphia, PA 19104 USA

年份：2012

卷号：164

期号：8

起止页码：1097

外文期刊名：JOURNAL OF APPROXIMATION THEORY

收录：;WOS:【SCI-EXPANDED(收录号:WOS:000306615200006)】；

基金：The research of the first author was supported by the National Natural Science Foundation of China (No. 11101146), the Fundamental Research Funds for the Central Universities and Scientific Research Foundation for the Returned Overseas Chinese Scholars, Ministry of Education, PR China. The research of the second author was partially supported by the National Science Foundation grants DMS 0542237 and DMS 1115915. Both authors thank Tom Duchamp for extensive discussions.

语种：英文

外文关键词：Nonlinear subdivision; Proximity condition; Manifold; Coordinate independence; Hermite-Biehler theorem

摘要：Proximity conditions are used extensively in the analysis of smoothness and approximation order properties of subdivision schemes for manifold-valued data. While these properties under question are independent of choice of coordinates on the manifold, it is not known whether the proximity condition itself is invariant under arbitrary change of coordinates. In this note, we answer this question to the affirmative, i.e. we prove that the proximity condition is satisfied in one coordinate system if and only if it is satisfied in any other coordinate system. In passing, we prove a connection between the general proximity condition and an alternate proximity condition used in the interpolatory case. This interpolatory proximity condition also enjoys the same invariance under change of coordinates. (C) 2012 Elsevier Inc. All rights reserved.