In this book, the authors provide general information on the subject of CR manifolds and the prerequisites from real and complex analysis. They develop the subjects of CR extension and the solvability of the tangential Cauchy-Riemann complex.
In this book, the authors provide general information on the subject of CR manifolds and the prerequisites from real and complex analysis. They develop the subjects of CR extension and the solvability of the tangential Cauchy-Riemann complex.
Part I: Preliminaries 1. Analysis on Euclidean Space 2. Analysis on Manifolds 3. Complexified Vectors and Forms 4. The Frobenius Theorem 5. Distribution Theory 6. Currents Part II: CR Manifolds 7. CR Manifolds 8. The Tangential Cauchy-Riemann Complex 9. CR Functions and Maps 10. The Levi Form 11. The Imbeddability of CR Manifolds 12. Further Results Part III: The Holomorphic Extension of CR Functions 13. An Approximation Theorem 14. The Statement of the CR Extension Theorem 15. The Analytic Disc Technique 16. The Fourier Transform Technique 17. Further Results Part IV: Solvability of the Tangential Cauchy-Riemann Complex 18. Kernel Calculus 19. Fundamental Solutions for the Exterior Derivative and Cauchy-Riemann Operators 20. The Kernels of Henkin 21. Fundamental Solutions for the Tangential Cauchy-Riemann Complex on a Convex Hypersurface 22. A Local Solution to the Tangential Cauchy-Riemann Equations 23. Local Nonsolvability of the Tangential Cauchy-Riemann Complex 24. Further Results
Part I: Preliminaries 1. Analysis on Euclidean Space 2. Analysis on Manifolds 3. Complexified Vectors and Forms 4. The Frobenius Theorem 5. Distribution Theory 6. Currents Part II: CR Manifolds 7. CR Manifolds 8. The Tangential Cauchy-Riemann Complex 9. CR Functions and Maps 10. The Levi Form 11. The Imbeddability of CR Manifolds 12. Further Results Part III: The Holomorphic Extension of CR Functions 13. An Approximation Theorem 14. The Statement of the CR Extension Theorem 15. The Analytic Disc Technique 16. The Fourier Transform Technique 17. Further Results Part IV: Solvability of the Tangential Cauchy-Riemann Complex 18. Kernel Calculus 19. Fundamental Solutions for the Exterior Derivative and Cauchy-Riemann Operators 20. The Kernels of Henkin 21. Fundamental Solutions for the Tangential Cauchy-Riemann Complex on a Convex Hypersurface 22. A Local Solution to the Tangential Cauchy-Riemann Equations 23. Local Nonsolvability of the Tangential Cauchy-Riemann Complex 24. Further Results
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