Exact inequalities and optimal recovery by inaccurate information

2025/04/12 by K. Yu. Osipenko, Osipenko, K. Yu.
Decision Sciences · Mathematics · #26DD15 #41A46 #41A65 #49N30 #Advanced Optimization Algorithms Research #FOS: Mathematics #Multi-Criteria Decision Making #Numerical Analysis (math.NA) #Risk and Portfolio Optimization

paper · pdf · doi:10.48550/arxiv.2504.09139

openalex publication_date 2025/04/12 · openalex created_date 2025/10/14 · openalex updated_date 2026/07/28

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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