齐次权加权空间的最优恢复

IF 0.8 4区数学 Q2 MATHEMATICS

Sbornik Mathematics Pub Date : 2022-01-01 DOI:10.1070/SM9475

K. Osipenko

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引用次数: 2

摘要

研究了齐次权加权空间中算子从噪声信息中恢复的问题。证明了一些一般定理，并将其应用于从噪声傅里叶变换中恢复微分算子的问题。特别地，得到了从-度规的噪声傅里叶变换中恢复拉普拉斯算子幂的最优方法。参考书目:30篇。

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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Optimal recovery in weighted spaces with homogeneous weights

The paper concerns problems of the recovery of operators from noisy information in weighted -spaces with homogeneous weights. A number of general theorems are proved and applied to problems of the recovery of differential operators from a noisy Fourier transform. In particular, optimal methods are obtained for the recovery of powers of the Laplace operator from a noisy Fourier transform in the -metric. Bibliography: 30 titles.

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来源期刊

Sbornik Mathematics 数学-数学

CiteScore

1.40

自引率

12.50%

发文量

审稿时长

6-12 weeks

期刊介绍： The Russian original is rigorously refereed in Russia and the translations are carefully scrutinised and edited by the London Mathematical Society. The journal has always maintained the highest scientific level in a wide area of mathematics with special attention to current developments in: Mathematical analysis Ordinary differential equations Partial differential equations Mathematical physics Geometry Algebra Functional analysis