Fourier 乘子 (Hörmander - Mihlin 乘子定理)

最新推荐文章于 2020-11-23 12:23:38 发布

转载最新推荐文章于 2020-11-23 12:23:38 发布 · 816 阅读

谱图论专栏收录该内容

7 篇文章

订阅专栏

本文深入探讨了卷积算子的收敛性质和范数估计，揭示了其与平移不变算子的等价性。通过傅里叶变换引入傅里叶乘子的概念，提供了一种研究卷积算子的新途径。

今天看到了这方面内容的描述，讲的比较好记录下来：https://zhuanlan.zhihu.com/p/111623179

摘取其中的一段：

1.Multipliers

In this section, we keep talk about the convergence property and norm estimate of convolution operator. In last section, we know some convolution operator can not be defined as usual Lebesgue integral but a limit process called singular integral. The stimulation of studying the convolution operator is that the convolution operator is equivalent to translation invariant operator.

Suppose $Tg=\int f\left ( x-y \right )g\left ( y \right )dy$ is a convolution operator. Then by Fourier transform, we have . The concept of multipliers give us another approach to study the convolution operator T: