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Zusatztext The book presents an up to date picture. Klappentext Rapid developments in multivariable spectral theory have led to important and fascinating results which also have applications in other mathematical disciplines. In this book, various concepts from function theory and complex analytic geometry are drawn together to give a new approach to concrete spectral computations and give insights into new developments in the spectral theory of linear operators. Classical results from cohomology theory of Banach algebras, multidimensional spectral theory, and complex analytic geometry have been freshly interpreted using the language of homological algebra. The advantages of this approach are illustrated by a variety of examples, unexpected applications, and conceptually new ideas that should stimulate further research among mathematicians. Zusammenfassung 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. Inhaltsverzeichnis Preface 1: Review of spectral theory 2: Analytic functional calculus via integral representations 3: Topological homology 4: Analytic sheaves 5: Fréchet modules over Stein algebras 6: Bishop's condition ( ) and invariant subspaces 7: Applications to function theory 8: Spectral analysis on Bergmann spaces 9: Finiteness theorems in analytic geometry 10: Multidimensional index theory Appendices: Locally convex spaces Homological algebra K-Theory and Riemann-Roch theorems Sobolev spaces References ...
