论文标题
周期性多元准插入式运算符的近似特性
Approximation properties of periodic multivariate quasi-interpolation operators
论文作者
论文摘要
我们研究了一般多元周期性准插入式操作员的近似属性，这些算子由分布/函数$ \widetildeφ_j$和三角多项式$φ_j$生成。此类操作员的类包括经典的插值多项式（$ \widetildeφ_j$是Dirac Delta函数），Kantorovich-Type运算符（$ \wideTildEdeφ_j$是一个特征函数），与小波构造以及其他相关的扩展。在$ \widetildeφ_j$和$φ_j$的不同兼容性条件下，我们获得了$ l_p $ - 近似值的估计值，即按Quasi-Interpolation Operators的近似值，以最佳和最佳的单方面近似，经典和分数的平滑度，$ K $ -Functionals和其他条款以及其他条款和其他条款。
We study approximation properties of general multivariate periodic quasi-interpolation operators, which are generated by distributions/functions $\widetildeφ_j$ and trigonometric polynomials $φ_j$. The class of such operators includes classical interpolation polynomials ($\widetildeφ_j$ is the Dirac delta function), Kantorovich-type operators ($\widetildeφ_j$ is a characteristic function), scaling expansions associated with wavelet constructions, and others. Under different compatibility conditions on $\widetildeφ_j$ and $φ_j$, we obtain upper and lower bound estimates for the $L_p$-error of approximation by quasi-interpolation operators in terms of the best and best one-sided approximation, classical and fractional moduli of smoothness, $K$-functionals, and other terms.
