平均维数，宽度，和最优恢复的索波列夫类的函数对线

Mathematics of The Ussr-sbornik Pub Date : 1993-02-28 DOI:10.1070/SM1993V074N02ABEH003352

G. Magaril-Il'yaev

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引用次数: 19

摘要

在广义子空间中引入了平均维数的概念，并定义了Kolmogorov宽度、Bernstein宽度、Gel'fand宽度和线性宽度的类似物。本文计算了相容度量上的Sobolev类函数的这些量的精确值，并描述了相应的极值空间和算子。研究了Sobolev类中函数的最优恢复问题。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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MEAN DIMENSION, WIDTHS, AND OPTIMAL RECOVERY OF SOBOLEV CLASSES OF FUNCTIONS ON THE LINE

The concept of mean dimension is introduced for a broad class of subspaces of , and analogues of the Kolmogorov widths, Bernstein widths, Gel'fand widths, and linear widths are defined. The precise values of these quantities are computed for Sobolev classes of functions on in compatible metrics, and the corresponding extremal spaces and operators are described. A closely related problem of optimal recovery of functions in Sobolev classes is also studied.

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Mathematics of The Ussr-sbornik

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