Charina M, Conti C, Guglielmi N, Protasov V
University of Vienna, Vienna, Austria.
DIEF-University of Florence, Florence, Italy.
Numer Math (Heidelb). 2017;135(3):639-678. doi: 10.1007/s00211-016-0809-y. Epub 2016 May 12.
In this paper, we study scalar multivariate non-stationary subdivision schemes with integer dilation matrix and present a unifying, general approach for checking their convergence and for determining their Hölder regularity (latter in the case [Formula: see text]). The combination of the concepts of asymptotic similarity and approximate sum rules allows us to link stationary and non-stationary settings and to employ recent advances in methods for exact computation of the joint spectral radius. As an application, we prove a recent conjecture by Dyn et al. on the Hölder regularity of the generalized Daubechies wavelets. We illustrate our results with several examples.
在本文中，我们研究具有整数膨胀矩阵的标量多元非平稳细分格式，并提出一种统一的通用方法来检验其收敛性以及确定其Hölder正则性（后者针对[公式：见正文]的情况）。渐近相似性和近似求和规则这两个概念的结合使我们能够将平稳和非平稳设置联系起来，并运用联合谱半径精确计算方法的最新进展。作为一个应用，我们证明了Dyn等人关于广义Daubechies小波的Hölder正则性的一个近期猜想。我们用几个例子来说明我们的结果。
