论文标题
使用剪切物的微局部分析和表征Sobolev波前集合
Microlocal analysis and characterization of Sobolev wavefront sets using shearlets
论文作者
论文摘要
Sobolev Wavefront集合和2美元的微粒子空间在描述和分析微局部分析和偏微分方程解决方案的分布奇点方面起着关键作用。在本文中，我们采用连续的剪切转换到Sobolev空间，在本文中，我们表征了微孔Sobolev Wavefront套件，$ 2 $ - 微粒子空间以及分布/功能的本地Hölder空间。然后，我们通过连续的剪切变换之间建立了Sobolev Wavefront集合，$ 2 $ - 微胶质空间和本地Hölder空间之间的连接。
Sobolev wavefront sets and $2$-microlocal spaces play a key role in describing and analyzing the singularities of distributions in microlocal analysis and solutions of partial differential equations. Employing the continuous shearlet transform to Sobolev spaces, in this paper we characterize the microlocal Sobolev wavefront sets, the $2$-microlocal spaces, and local Hölder spaces of distributions/functions. We then establish the connections among Sobolev wavefront sets, $2$-microlocal spaces, and local Hölder spaces through the continuous shearlet transform.
