Hyperfunctions on Hypo-Analytic Manifolds
Seiten
1994
Princeton University Press (Verlag)
978-0-691-02993-1 (ISBN)
Princeton University Press (Verlag)
978-0-691-02993-1 (ISBN)
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This monograph expounds the theory of hyperfunctions on totally real submanifolds of multidimensional complex space, in particular of hyperfunction theory in real space. It then defines the hypoanalytic wave-front set and the Fourier-Bros-Iagolnitzer transform of a hyperfunction.
In the first two chapters of this book, the reader will find a complete and systematic exposition of the theory of hyperfunctions on totally real submanifolds of multidimensional complex space, in particular of hyperfunction theory in real space. The book provides precise definitions of the hypoanalytic wave-front set and of the Fourier-Bros-Iagolnitzer transform of a hyperfunction. These are used to prove a very general version of the famed Theorem of the Edge of the Wedge. The last two chapters define the hyperfunction solutions on a general (smooth) hypo-analytic manifold, of which particular examples are the real analytic manifolds and the embedded CR manifolds. The main results here are the invariance of the spaces of hyperfunction solutions and the transversal smoothness of every hyperfunction solution. From this follows the uniqueness of solutions in the Cauchy problem with initial data on a maximally real submanifold, and the fact that the support of any solution is the union of orbits of the structure.
In the first two chapters of this book, the reader will find a complete and systematic exposition of the theory of hyperfunctions on totally real submanifolds of multidimensional complex space, in particular of hyperfunction theory in real space. The book provides precise definitions of the hypoanalytic wave-front set and of the Fourier-Bros-Iagolnitzer transform of a hyperfunction. These are used to prove a very general version of the famed Theorem of the Edge of the Wedge. The last two chapters define the hyperfunction solutions on a general (smooth) hypo-analytic manifold, of which particular examples are the real analytic manifolds and the embedded CR manifolds. The main results here are the invariance of the spaces of hyperfunction solutions and the transversal smoothness of every hyperfunction solution. From this follows the uniqueness of solutions in the Cauchy problem with initial data on a maximally real submanifold, and the fact that the support of any solution is the union of orbits of the structure.
François Treves is the Robert Adrain Professor of Mathematics at Rutgers University. Paulo D. Cordaro is Associate Professor of Mathematics at the University of Sao Paulo in Brazil.
| Reihe/Serie | Annals of Mathematics Studies |
|---|---|
| Verlagsort | New Jersey |
| Sprache | englisch |
| Maße | 197 x 254 mm |
| Gewicht | 482 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Geometrie / Topologie |
| ISBN-10 | 0-691-02993-8 / 0691029938 |
| ISBN-13 | 978-0-691-02993-1 / 9780691029931 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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