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 contains a variety of illustrative examples, unexpected applications, and exciting new ideas which should stimulate further research. Written by two outstanding mathematicians, the book draws together concepts from function theory and complex analytical geometry and uses these to provide a new approach to concrete spectral computations.