Microlocal analysis and characterization of Sobolev wavefront sets using shearlets
Functional Analysis
2020-10-12 v2 Analysis of PDEs
Abstract
Sobolev wavefront sets and -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 -microlocal spaces, and local H\"older spaces of distributions/functions. We then establish the connections among Sobolev wavefront sets, -microlocal spaces, and local H\"older spaces through the continuous shearlet transform.
Keywords
Cite
@article{arxiv.2003.06762,
title = {Microlocal analysis and characterization of Sobolev wavefront sets using shearlets},
author = {Bin Han and Swaraj Paul and Niraj K. Shukla},
journal= {arXiv preprint arXiv:2003.06762},
year = {2020}
}
Comments
Accepted in Constructive Approximation