An Introduction to Involutive Structures

by Shiferaw Berhanu, Paulo D. Cordaro, Jorge Hounie

Overview

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.

Product Details

ISBN-13:	9780521878579
Publisher:	Cambridge University Press
Publication date:	03/20/2008
Series:	New Mathematical Monographs , #6
Pages:	404
Product dimensions:	6.30(w) x 9.25(h) x 0.98(d)

About the Author

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.

Table of Contents

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.

Editorial Reviews

"The choice of topics and the exposition (the authors are renowned experts in the field, and are well known for their clarity) make this book really beautiful."
Alberto Parmeggiani, Mathematical Reviews

From the Publisher