An Introduction to Involutive Structures(ISBN=9780521878579) 2025 chm pdf kindle rb azw3 下载 115盘

　　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

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书籍介绍

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.