Journal article

Publication year: 2006

Pages: 211-235

Journal: Advances in Computational Mathematics

Volume number: 25

Issue number: 1-3

ISSN: 1019-7168

eISSN: 1572-9044

DOI Link: https://doi.org/10.1007/s10444-004-7635-y

Publisher: Springer

Abstract: 
The paper develops a necessary condition for the regularity of a multivariate refinable function in terms of a factorization property of the associated subdivision mask. The extension to arbitrary isotropic dilation matrices necessitates the introduction of the concepts of restricted and renormalized convergence of a subdivision scheme as well as the notion of subconvergence, i.e., the convergence of only a subsequence of the iterations of the subdivision scheme. Since, in addition, factorization methods pass even from scalar to matrix valued refinable functions, those results have to be formulated in terms of matrix refinable functions or vector subdivision schemes, respectively, in order to be suitable for iterated application. Moreover, it is shown for a particular case that the the condition is not only a necessary but also a sufficient one.

Harvard Citation style: Sauer, T. (2006) Differentiability of multivariate refinable functions and factorization, Advances in Computational Mathematics, 25(1-3), pp. 211-235. https://doi.org/10.1007/s10444-004-7635-y

APA Citation style: Sauer, T. (2006). Differentiability of multivariate refinable functions and factorization. Advances in Computational Mathematics. 25(1-3), 211-235. https://doi.org/10.1007/s10444-004-7635-y