Microlocal analysis of lagrangian submanifolds of radial points
Abstract/Contents
- Abstract
- Microlocal analysis relies on correspondences between quantum physics and classical physics to give information about certain PDEs -- for instance, linear variable-coefficient PDEs on manifolds. PDEs are interpreted as quantum systems. The corresponding classical systems tell us, for example, function spaces on which problems are solvable or almost solvable, existence and uniqueness results, and the structure of solution operators. Landmark papers of Hörmander and Duistermaat and Hörmander establish key results for the standard calculus of microlocal analysis, which gives a broad framework for dealing with variable-coefficient PDEs on manifolds. Their work is well-suited for dealing with PDEs which, in a generalized sense, are hyperbolic, with corresponding classical dynamics looking like wave propagation of geometric optics. In this thesis, we aim to extend many of their results to situations in which the corresponding classical dynamics are less well-behaved: those with a Lagrangian submanifold of radial points.
Description
| Type of resource | text |
|---|---|
| Form | electronic; electronic resource; remote |
| Extent | 1 online resource. |
| Publication date | 2013 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Associated with | Haber, Nick |
|---|---|
| Associated with | Stanford University, Department of Mathematics. |
| Primary advisor | Vasy, András |
| Thesis advisor | Vasy, András |
| Thesis advisor | Brendle, Simon, 1981- |
| Thesis advisor | Mazzeo, Rafe |
| Thesis advisor | Venkatesh, Akshay, 1981- |
| Advisor | Brendle, Simon, 1981- |
| Advisor | Mazzeo, Rafe |
| Advisor | Venkatesh, Akshay, 1981- |
Subjects
| Genre | Theses |
|---|
Bibliographic information
| Statement of responsibility | Nick Haber. |
|---|---|
| Note | Submitted to the Department of Mathematics. |
| Thesis | Thesis (Ph.D.)--Stanford University, 2013. |
| Location | electronic resource |
Access conditions
- Copyright
- © 2013 by Nicholas Joseph Haber
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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