Regularization of distributions

IF 0.8 4区数学 Q2 MATHEMATICS

Sbornik Mathematics Pub Date : 2023-01-01 DOI:10.4213/sm9803e

Aleksandr Leonidovich Pavlov

引用次数: 0

Abstract

Sufficient conditions are presented for the construction of a regularization of a distribution in the form $a(\sigma)f$, where $f$ is a distribution and $a(\sigma)$ is an infinitely differentiable function outside a closed set $N$ which has power-like singularities of derivatives on $N$. Applications of such regularizations to an effective construction of solutions of the equation $Pu=f$, where $P(\sigma)$ is a polynomial, are considered. Bibliography: 14 titles.

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分布的正则化

给出了构造正则化形式为$a(\sigma)f$的分布的充分条件，其中$f$是一个分布，$a(\sigma)$是一个在$N$上有幂次导数奇点的闭集$N$外的无穷可微函数。考虑了这种正则化在方程$Pu=f$解的有效构造中的应用，其中$P(\sigma)$是一个多项式。参考书目:14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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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