caa a22 4500 467939438 CHVBK 20180406153007.0 cr unu---uuuuu 170328e20060701xx s 000 0 eng 10.1007/s10444-004-7635-y doi (NATIONALLICENCE)springer-10.1007/s10444-004-7635-y Sauer Thomas Lehrstuhl für Numerische Mathematik, Justus-Liebig-Universität Giessen, Heinrich-Buff-Ring 44, D-35392, Giessen, Germany aut Differentiability of multivariate refinable functions and factorization [Elektronische Daten] [Thomas Sauer] 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. Springer, 2006 subdivision nationallicence refinable function nationallicence subconvergence nationallicence Advances in Computational Mathematics Kluwer Academic Publishers 25/1-3(2006-07-01), 211-235 1019-7168 25:1-3<211 2006 25 10444 https://doi.org/10.1007/s10444-004-7635-y text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10444-004-7635-y text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Sauer Thomas Lehrstuhl für Numerische Mathematik, Justus-Liebig-Universität Giessen, Heinrich-Buff-Ring 44, D-35392, Giessen, Germany aut NATIONALLICENCE 773 0- Advances in Computational Mathematics Kluwer Academic Publishers 25/1-3(2006-07-01), 211-235 1019-7168 25:1-3<211 2006 25 10444 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer