The X-ray transform on asymptotically euclidean spaces
Abstract/Contents
- Abstract
- The x-ray problem is a linear inverse problem which asks if a function can be determined from its integral along a class of curves. This thesis goes through a brief history including the x-ray transform's relationship to nonlinear problems such as boundary distance rigidity. It provides an introduction to microlocal analysis and the scattering algebra, before intro- ducing a new algebra similar to the scattering algebra. Using this new algebra, a modified x-ray transform on asymptotically Euclidean spaces is a locally elliptic operator in this new setting. This ellipticity in turn shows that the original x-ray transform has a left inverse up to a finite rank error in a region near infinity on asymptotically Euclidean spaces
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 | Zachos, Evangelie May Leurgans |
|---|---|
| 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 | Evangelie Zachos |
|---|---|
| Note | Submitted to the Department of Mathematics |
| Thesis | Thesis Ph.D. Stanford University 2020 |
| Location | electronic resource |
Access conditions
- Copyright
- © 2020 by Evangelie May Leurgans Zachos
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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