Abstract
Our results describe how quantitative properties of univariate operators are inherited by the tensor product of their parametric extensions. This includes statements concerning simultaneous approximation. The estimates are in terms of partial and total moduli of smoothness of higher order. Applications are given for cubic interpolatory splines and Bernstein operators. Further applications are possible.
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Beutel, L., Gonska, H.H. Quantitative Inheritance Properties for Simultaneous Approximation by Tensor Product Operators. Numerical Algorithms 33, 83–92 (2003). https://doi.org/10.1023/A:1025539316792
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DOI: https://doi.org/10.1023/A:1025539316792