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Description
(Text)
Integrale Darstellungen von Funktionen und Differentialformen sind ein wichtiges Werkzeug, um quantitative Resultate für holomorphe Funktionen auf komplexen Mannigfaltigkeiten zu entwickeln. Dieses Buch ist eine Monographie zu einem Spezialgebiet der komplexen Analysis.
(Short description)
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.
(Text)
The main topics presented in this research monograph from the field of Complex Analysis are:
Cauchy-Fantappie integrals, fundamental solutions in complex analysis,
holomorphic integral formulae, solution of the Cauchy-Riemann equations with
precise (subelliptic and Hoelder subelliptic) estimates and integral
representation of the Neumann operator on strictly pseudoconvex manifolds,
application to the Levi problem, further applications to approximation,
decompostion and extension problems of complex analysis.
The book can also be used in an advanced seminar for graduate students.
(Table of content)
From the Contents:
-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
(Author portrait)
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.
