Abstract The article presents an explicit form for the second moment of cubic Schoenberg operators with arbitrary knots and in the particular case of equidistant knots. Applications are given for quantitative direct results in approximation and in construction of special classes of Schoenberg operators.

中文翻译：

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三阶勋伯格样条算子的二阶矩的精确形式

摘要 本文提出了具有任意节点的三次勋伯格算子的二阶矩的明确形式，并且在等距节点的特殊情况下。在近似和构造特殊类别的勋伯格算子中给出了定量直接结果的应用。