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arXiv · 2504.09139

Exact inequalities and optimal recovery by inaccurate information

K. Yu. Osipenko
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Abstract

The paper considers a multidimensional problem of optimal recovery of an operator whose action is represented by multiplying the original function by a weight function of a special type, based on inaccurately specified information about the values of operators of a similar type. An exact inequality for the norms of such operators is obtained. The problem under consideration is a generalization of the problem of optimal recovery of a derivative based on other inaccurately specified derivatives in the space $\mathbb R^d$ and the problem of an exact inequality, which is an analogue of the Hardy-Littlewood-Polya inequality.

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K. Yu. Osipenko. 2025-04-12. Exact inequalities and optimal recovery by inaccurate information. https://arxiv.org/abs/2504.09139

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