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Ziel dieses Lehrbuches ist es, einen verstandlichen, moeglichst direkten und in sich geschlossenen Zugang zu wichtigen Ergebnissen der mehrdimensionalen Funktionentheorie zu geben. Hierbei fuhrt der Weg von elementaren Eigenschaften holomorpher Funktionen uber analytische Mengen und Holomorphiebereiche bis hin zum Levi-Problem. Ein abschliessendes Kapitel enthalt mit der Konstruktion des mehrdimensionalen holomorphen Funktionalkalkuls nach Shilov, Waelbroeck und Arens-Calderon und dem Satz von Arens-Royden wichtige Anwendungen auf die Theorie komplexer Banachalgebren. Zahlreiche UEbungsaufgaben erganzen den theoretischen Teil. Vorausgesetzt wird nur der Inhalt der Grundvorlesungen in Analysis und einer ublichen einsemestrigen Vorlesung uber Funktionentheorie einer komplexen Veranderlichen. Das Buch richtet sich besonders an fortgeschrittene Bachelorstudierende oder Studierende eines Masterstudienganges und eignet sich bestens als Begleitlekture zu einer Vorlesung oder auch zum Selbststudium.
Based on lectures given at an instructional course, this volume enables readers with a basic knowledge of functional analysis to access key research in the field. The authors survey several areas of current interest, making this volume ideal preparatory reading for students embarking on graduate work as well as for mathematicians working in related areas.
Based on lectures given at an instructional course, this volume enables readers with a basic knowledge of functional analysis to access key research in the field. The authors survey several areas of current interest, making this volume ideal preparatory reading for students embarking on graduate work as well as for mathematicians working in related areas.
Rapid developments in multivariable spectral theory have led to important and fascinating results which also have applications in other mathematical disciplines. In this book, classical results from the cohomology theory of Banach algebras, multidimensional spectral theory, and complex analytic geometry have been freshly interpreted using the language of homological algebra. It has also been used to give in sights into new developments in the spectral theory of linear operators. Various concepts from function theory and complex analytic geometry are drawn together and used to give a new approach to concrete spectral computations. The advantages of this approach are illustrated by a variety of examples, unexpected applications, and conceptually new ideas which should stimulate further research.
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