The d-bar Neumann Problem and Schr#x000F6;dinger Operators

The topic of this bookis 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.