Radial estimate of isotropic pseudo-differential operators via FBI transform
Abstract/Contents
- Abstract
- This works aims to prove the propagation of singularities and the radial estimates in smooth isotropic symbol settings. The behavior of the Hamilton vector field of pseudo differential operator symbols and the wave front set of the solutions has been well studied. There are classical results in the standard smooth symbols settings, linking the flow of the Hamilton vector field of the symbol with the operator's regularity propagation by Hörmander. Melrose and Vasy then also establish the regularity behavior of solutions around radial points when it forms a sink or source for the Hamilton vector field. This paper extends such results into the setting of isotropic symbols. First setting up the connections between the isotropic and standard symbols, the paper will then utilize the FBI transform mechanisms, similar to the work of Martinez, to achieve results similar to the standard commutator method. Then we shall refine the results in the isotropic setting from Martinez's FBI estimate. Finally a standard regularization process shall be deployed to establish the more precise high regularity threshold
Description
| Type of resource | text |
|---|---|
| Form | electronic resource; remote; computer; online resource |
| Extent | 1 online resource |
| Place | California |
| Place | [Stanford, California] |
| Publisher | [Stanford University] |
| Copyright date | 2020; ©2020 |
| Publication date | 2020; 2020 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Author | Zhu, Beite |
|---|---|
| Degree supervisor | Vasy, András |
| Thesis advisor | Vasy, András |
| Thesis advisor | Luk, Jonathan, (Professor) |
| Thesis advisor | Mazzeo, Rafe |
| Degree committee member | Luk, Jonathan, (Professor) |
| Degree committee member | Mazzeo, Rafe |
| Associated with | Stanford University, Department of Mathematics |
Subjects
| Genre | Theses |
|---|---|
| Genre | Text |
Bibliographic information
| Statement of responsibility | Beite Zhu |
|---|---|
| Note | Submitted to the Department of Mathematics |
| Thesis | Thesis Ph.D. Stanford University 2020 |
| Location | electronic resource |
Access conditions
- Copyright
- © 2020 by Beite Zhu
- License
- This work is licensed under a Creative Commons Attribution 3.0 Unported license (CC BY).
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