The d-bar Neumann Problem and Schrödinger Operators
| Autor: | Friedrich Haslinger |
|---|---|
| EAN: | 9783110315356 |
| eBook Format: | ePUB/PDF |
| Sprache: | Englisch |
| Produktart: | eBook |
| Veröffentlichungsdatum: | 20.08.2014 |
| Untertitel: | d-bar Neumann Problem and Schrödinger Operators |
| Kategorie: | |
| Schlagworte: | Funktionentheorie Neumannproblem Schrödingeroperator d-bar Neumann Problem; Inhomogeneous Cauchy-Riemann Equation; Hankel Operator; Compactness; Schrödinger Operator; Witten Laplacian |
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The topic of this book is located at the intersection of complex analysis, operator theory and partial differential equations. First we investigate the canonical solution operator to d-bar restricted to Bergman spaces of holomorphic L2 functions in one and several complex variables. These operators are Hankel operators of special type. In the following we consider the general d-bar-complex and derive properties of the complex Laplacian on L2 spaces of bounded pseudoconvex domains and on weighted L2 spaces.
The main part is devoted to compactness of the d-bar-Neumann operator. The last part will contain a detailed account of the application of the d-bar-methods to Schrödinger operators, Pauli and Dirac operators and to Witten-Laplacians.
Friedrich Haslinger, University of Vienna, Austria.
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