论文标题
多变量紧凑型$ C^\ infty $函数由细分
Multivariate compactly supported $C^\infty$ functions by subdivision
论文作者
论文摘要
本文讨论了由细分方案与紧凑的小支持的多元$ c^\ infty $函数的生成。在构建这样的单变量函数后，通过基于生长程度的{spline SupDivision SupDivision Schemes}的掩模的非平稳方案称为\ emph {up功能}，我们将其称为多变量函数我们生成的up-like函数。我们通过基于不断增长的支撑箱的箱形掩膜来通过非平稳方案生成它们。为了分析这些非平稳方案的收敛性和平滑性，我们开发了适用于比我们研究的类更宽的方案类别的新工具。通过我们实现小紧凑型支撑的方法，我们在单变量的情况下获得了类似于支持$ [0，1 +ε] $的UPING函数，与支持$ [0，2] $相比。给出了单变量和双变量向上功能的示例。就像在单变量的情况下一样，上升函数的构建可以激发$ c^\ infty $紧凑型$支持的小波在任何维度上的小小支撑。
This paper discusses the generation of multivariate $C^\infty$ functions with compact small supports by subdivision schemes. Following the construction of such a univariate function, called \emph{Up-function}, by a non-stationary scheme based on masks of {spline subdivision schemes} of growing degrees, we term the multivariate functions we generate Up-like functions. We generate them by non-stationary schemes based on masks of box-splines of growing supports. To analyze the convergence and smoothness of these non-stationary schemes, we develop new tools which apply to a wider class of schemes than the class we study. With our method for achieving small compact supports, we obtain, in the univariate case, Up-like functions with supports $[0, 1 +ε]$ in comparison to the support $[0, 2] $ of the Up-function. Examples of univariate and bivariate Up-like functions are given. As in the univariate case, the construction of Up-like functions can motivate the generation of $C^\infty$ compactly supported wavelets of small support in any dimension.
