Bibliographic Details
| Title: |
Compactness in the \(\overline\partial\)-Neumann problem, magnetic Schrödinger operators, and the Aharonov-Bohm effect |
| Authors: |
Christ, Michael, Fu, Siqi |
| Publisher Information: |
Elsevier (Academic Press), San Diego, CA |
| Subject Terms: |
condition (P), \(\overline \partial\)-Neumann operator, \(\overline\partial\)-Neumann problems and formal complexes in context of PDEs, Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory, \(\overline\partial\) and \(\overline\partial\)-Neumann operators, Schrödinger operators |
| Description: |
The condition (P) on a pseudoconvex domain \(\Omega\) means that for any \(M>0\) there is a smooth plurisubharmonic function \(\lambda\) with \(0\leq \lambda \leq 1\) such that for all \(z\in \partial \Omega\): \[ \sum _{j,k=1}^{n} \frac {\partial^2 \lambda}{\partial z_j\partial \overline z_k} t_j\overline t_k\geq M| t| ^2, \quad \forall t=(t_1,t_2,\cdots ,t_n)\in \mathbb{C}^n, \] which was introduced by \textit{D. W. Catlin} [Proc. Sympos. Pure Math. 41, 39--49 (1984; Zbl 0578.32031)] to prove the compactness of the \(\overline \partial\)-Neumann operator. In order to have more clear picture about the relation between the condition (P) and the compactness of the \(\overline \partial\)-Neumann operator, Hartogs domain in \(\mathbb C^2\) is a good example to look at. Let \[ \Omega =\{(z,w)\in \mathbb C^2 :| w |
| Document Type: |
Article |
| File Description: |
application/xml |
| DOI: |
10.1016/j.aim.2004.08.015 |
| Access URL: |
https://zbmath.org/2217899 |
| Accession Number: |
edsair.c2b0b933574d..dc7ba711552df05ac2073f7a0a3fc8be |
| Database: |
OpenAIRE |