An Introduction to Involutive Structures

Detailing the main methods in the theory of involutive systems of complex vector fields this book examines the major results from the last twenty five years in the subject. One of the key tools of the subject - the Baouendi-Treves approximation theorem - is proved for many function spaces. This in turn is applied to questions in partial differential equations and several complex variables. Many basic problems such as regularity, unique continuation and boundary behaviour of the solutions are explored. The local solvability of systems of partial differential equations is studied in some detail. The book provides a solid background for others new to the field and also contains a treatment of many recent results which will be of interest to researchers in the subject.

Shiferaw Berhanu is a Professor of Mathematics at Temple University in Philadelphia.

Paulo D. Cordaro is a Professor of Mathematics in the Institute of Mathematics and Statistics at the University of São Paulo.

Jorge Hounie is a Professor of Mathematics at the Federal University of São Carlos in Brazil.