Spectral Decompositions and Analytic Sheaves

This monograph uses the language of homological algebra and sheaf theory to describe both classical results and recent developments in the spectral theory of linear operators. It draws together concepts from function theory and complex analytical geometry.
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.