The method of integral representations is developed in order to establish 1. classical fundamental results of complex analysis both elementary and advanced, 2. subtle existence and regularity theorems for the Cauchy-Riemann equations on complex manifolds. These results are then applied to important function theoretic questions. The book can be used for advanced courses and seminars at the graduate level; it contains to a large extent material which has not yet been covered in text books.
Autorentext
Prof. Dr. Ingo Lieb ist Professor für Mathematik an der Universität Bonn. Er ist Autor der beiden Bücher "Funktionentheorie" und "Ausgewählte Kapitel aus der Funktionentheorie" in der Reihe vieweg studium/Aufbaukurs Mathematik.
Prof. Dr. Joachim Michel ist Professor für Mathematik am "Laboratoire de Mathématiques Pures et Appliquées Joseph Liouville" (L.M.P.A.) in Calais, Frankreich.
Inhalt
The Bochner-Martinelli formula - The Koppelman calculus - Strictly pseudoconvex domains and Levi's problem - Hodge theory on compact manifolds - Levi s problem on strictly pseudoconvex manifolds - Friedrichs' extension lemma and formulation of the Neumann problem - Solution of the Neumann problem on strictly pseudoconvex manifolds - Applications - Function spaces and regularity of integral operators.