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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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