论从函数谱的近似信息中优化恢复一类函数上的一个算子族

IF 0.7 4区数学 Q2 MATHEMATICS

Siberian Mathematical Journal Pub Date : 2024-03-25 DOI:10.1134/s0037446624020010

E. V. Abramova, E. O. Sivkova

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引用次数: 0

摘要

我们从以下信息中找到了在恢复索博廖夫函数类上连续线性算子值问题中最优恢复方法的明确表达式：在函数被定义的有限维空间的某个可测量子集上，函数的傅立叶变换是近似已知的。作为推论，我们得到了恢复heatequation 的解和求解半空间的 Dirichlet 问题的最优方法。

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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On the Optimal Recovery of One Family of Operators on a Class of Functions from Approximate Information about Its Spectrum

We find explicit expressions for optimal recovery methods in the problem of recovering the values of continuous linear operators on a Sobolev function class from the following information: The Fourier transform of functions is known approximately on some measurable subset of the finite-dimensional space on which the functions are defined. As corollaries, we obtain optimal methods for recovering the solution to the heat equation and solving the Dirichlet problem for a half-space.

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来源期刊

Siberian Mathematical Journal 数学-数学

CiteScore

1.00

自引率

20.00%

发文量

审稿时长

4-8 weeks

期刊介绍： Siberian Mathematical Journal is journal published in collaboration with the Sobolev Institute of Mathematics in Novosibirsk. The journal publishes the results of studies in various branches of mathematics.