论文标题
多变量瓷砖B-Splines
Multivariate tile B-splines
论文作者
论文摘要
$ \ mathbb {r}^d $中的瓷砖b-splines定义为瓷砖指标的自动vol，它们是特殊的自相似紧凑型集合，其整数将瓷砖转换为空间$ \ mathbb {r}^d $。这些功能不是分段多项式的，但是是对古典B型规模的直接概括，它们享有许多属性，并且具有一些优势。特别是，在这项工作中计算了瓷砖B-splines的Hölder指数的精确值。它们有时会超过经典B-Splines的规律性。构建了基于瓷砖B型的小波的正交系统，并获得了其衰减的估计值。瓷砖B型构建的细分方案证明了它们在应用中的效率。它是通过高规律性，快速收敛性和相应细化方程中的少量系数来实现的。
Tile B-splines in $\mathbb{R}^d$ are defined as autoconvolutions of the indicators of tiles, which are special self-similar compact sets whose integer translates tile the space $\mathbb{R}^d$. These functions are not piecewise-polynomial, however, being direct generalizations of classical B-splines, they enjoy many of their properties and have some advantages. In particular, the precise values of the Hölder exponents of the tile B-splines are computed in this work. They sometimes exceed the regularity of the classical B-splines. The orthonormal systems of wavelets based on the tile B-splines are constructed and the estimates of their exponentional decay are obtained. Subdivision schemes constructed by the tile B-splines demonstrate their efficiency in applications. It is achieved by means of the high regularity, the fast convergence, and small number of the coefficients in the corresponding refinement equation.
