An introduction to involutive structures
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Bibliographic Information
An introduction to involutive structures
（New mathematical monographs, 6）
Cambridge University Press, 2008
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
BER||112||1200005161460
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Note
Includes bibliographical references and index
Description and Table of Contents
Description
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.
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.
by "Nielsen BookData"