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Approximation properties of periodic multivariate quasi-interpolation operators
Journal of Approximation Theory ( IF 0.9 ) Pub Date : 2021-07-18 , DOI: 10.1016/j.jat.2021.105631
Yurii Kolomoitsev 1 , Jürgen Prestin 1
Affiliation  

We study approximation properties of general multivariate periodic quasi-interpolation operators, which are generated by distributions/functions φ˜j and trigonometric polynomials φj. The class of such operators includes classical interpolation polynomials (φ˜j is the Dirac delta function), Kantorovich-type operators (φ˜j is a characteristic function), scaling expansions associated with wavelet constructions, and others. Under different compatibility conditions on φ˜j and φj, we obtain upper and lower bound estimates for the Lp-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.



中文翻译:

周期多元拟插值算子的逼近性质

我们研究了由分布/函数生成的一般多元周期性准插值算子的近似性质 φj 和三角多项式 φj. 此类运算符包括经典插值多项式 (φj 是狄拉克 delta 函数),Kantorovich 型运算符(φj是一个特征函数)、与小波构造相关的缩放扩展等。在不同的兼容条件下φjφj,我们获得了上限和下限估计 - 准插值算子在最佳和最佳单边近似、经典和分数平滑模量方面的近似误差, -泛函和其他术语。

更新日期:2021-07-19
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