论文标题
准互化运算符和Smolyak的算法近似
Approximation by quasi-interpolation operators and Smolyak's algorithm
论文作者
论文摘要
我们研究了使用Kantorovich-type的特殊类别的准交互操作员构建的Smolyak算法来支配混合平滑度的多元周期函数的近似。这些运算符的定义与经典采样运算符相似，通过用较小的间隔替换函数的平均值（或更一般而言，用适当的内核的给定函数卷积的采样值）。在本文中，我们估计了来自besov spaces $ \ mathbf {b} _ {p，θ}^s（\ mathbb {t}^d）$ \ mathbf {b} $ \ mathbf {b} $ \ mathbf {b} _ $ \ mathbf {f} _ {p，θ}^s（\ mathbb {t}^d）$对于所有$ s> 0 $和可允许的$ 1 \ le P，θ\ le \ le \ infty $，并提供了这些Quasition of quasie forder of quasie foreplywood-paley-paley-type的类似物的类似物。
We study approximation of multivariate periodic functions from Besov and Triebel--Lizorkin spaces of dominating mixed smoothness by the Smolyak algorithm constructed using a special class of quasi-interpolation operators of Kantorovich-type. These operators are defined similar to the classical sampling operators by replacing samples with the average values of a function on small intervals (or more generally with sampled values of a convolution of a given function with an appropriate kernel). In this paper, we estimate the rate of convergence of the corresponding Smolyak algorithm in the $L_q$-norm for functions from the Besov spaces $\mathbf{B}_{p,θ}^s(\mathbb{T}^d)$ and the Triebel--Lizorkin spaces $\mathbf{F}_{p,θ}^s(\mathbb{T}^d)$ for all $s>0$ and admissible $1\le p,θ\le \infty$ as well as provide analogues of the Littlewood--Paley-type characterizations of these spaces in terms of families of quasi-interpolation operators.
