Detailing the main methods in the theory of involutive systems of complex vector fields, this book examines the major results from the last 25 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 behavior 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 beginners in the field and also contains a treatment of many recent results which will be of interest to researchers in the subject.
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.
The main tools of involutive systems of complex vector fields together with the major results from last twenty five years.
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' 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
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The main tools of involutive systems of complex vector fields together with the major results from last twenty five years.
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.
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.
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