Title: The [D-bar] Neumann problem and Schrödinger operators
Description: The topic of this book is located at the intersection of complex analysis, operator theory and partial differential equations. It begins with results on 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 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. It is assumed that the reader has a basic knowledge of complex analysis, functional analysis and topology. With minimal prerequisites required, this book provides a systematic introduction to an active area of research for both students at a bachelor level and mathematicians.
Subjects: Neumann problem, Schrödinger operator, Boundary value problems, Differential operators