An Introduction to Involutive Structures

The main tools of involutive systems of complex vector fields together with the major results from last twenty five years.

Shiferaw Berhanu (Author), Paulo D. Cordaro (Author), Jorge Hounie (Author)

9780521878579, Cambridge University Press

Hardback, published 20 March 2008

404 pages
23.5 x 16 x 2.5 cm, 0.7 kg

'… carefully organised … The book will be very useful for students wanting to learn the subject and it also introduces interesting recent results for specialists.' EMS Newsletter

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.

Preface
1. Locally integrable structures
2. The Baouendi-Treves approximation formula
3. Sussmann's orbits and unique continuation
4. Local solvability of vector fields
5. The FBI transform and some applications
6. Some boundary properties of solutions
7. The differential complex associated to a formally integrable structure
8. Local solvability in locally integrable structures
Epilogue
Bibliography
A. Hardy space lemmas.

Subject Areas: Complex analysis, complex variables [PBKD]