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Abstract <p> A new definition of the derivative of variable order is given based on the interpolation of derivatives of natural order. For the joint interpolation of a function and its derivative of variable order, interpolation operators of Hermite–Fejér type are constructed in the one-dimensional and multidimensional cases. Upper bounds for the norms of these operators in the one-dimensional and multidimensional periodic Sobolev spaces are obtained. It is shown that, in the one-dimensional case, the norm of this operator is bounded. In the multidimensional case, the upper bound depends on the ratio of the number of nodes for each coordinate. </p>

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Estimation of the Norm of the Hermite–Fejér Interpolation Operator with Variable Order Derivatives in Sobolev Spaces

  • 期刊论文

  • 发表日期：

    2025年2月1日

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  • A. I. Fedotov

摘要

Abstract

A new definition of the derivative of variable order is given based on the interpolation of derivatives of natural order. For the joint interpolation of a function and its derivative of variable order, interpolation operators of Hermite–Fejér type are constructed in the one-dimensional and multidimensional cases. Upper bounds for the norms of these operators in the one-dimensional and multidimensional periodic Sobolev spaces are obtained. It is shown that, in the one-dimensional case, the norm of this operator is bounded. In the multidimensional case, the upper bound depends on the ratio of the number of nodes for each coordinate.