The d-bar Neumann Problem and Schrödinger Operators

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<p>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&#xa0; restricted to<br>Bergman spaces of holomorphic d-bar functions in one and several complex variables.These operators are Hankel operators of special type. In the following the general&#xa0; complex is investigated on&#xa0;d-bar spaces over bounded pseudoconvex domains and on weighted&#xa0;d-bar spaces. The main part is devoted to the spectral analysis of the complex Laplacian and to compactness of the&#xa0; Neumann operator.<br>The last part contains a detailed account of the application of the&#xa0; 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&#xa0; 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.<br></p>