Complexes of Differential Operators

the long version

The main topic of Complexes of Differential Operators is the study of general complexes of differential operators between sections of vector bundles. Although the global situation and the local one (i.e., complexes of partial differential operators on an open subset of Rn) are often similar in content, the invariant language permits the simplification of the notation and more clearly reveals the algebraic structure of some questions. All of the recent developments in the theory of complexes of differential operators are dealt with to some degree: formal theory; existence theory; global solvability problem; overdetermined boundary problems; generalised Lefschetz theory of fixed points; qualitative theory of solutions of overdetermined systems. Considerable attention is paid to the theory of functions of several complex variables. Includes many examples and exercises. Audience: Mathematicians, physicists and engineers studying the analysis of manifolds, partial differential equations and several complex variables.