Hyperfunctions on Hypo-Analytic Manifolds {AM - 136} (Annals of Mathematics Studies, 136) - Softcover

Cordaro, Paulo

Softcover

ISBN 10: 069102992X ISBN 13: 9780691029924

Publisher: Princeton University Press, 1994

Synopsis

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 hypo-analytic 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.

About this title

About the Author

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.

From the Back Cover

The material in the present monograph represents, in a sense, the next logical step in the development of the local (and microlocal) theory of hypo-analytic structures described in the book [TREVES, 1992]. The theory developed here relies on concepts, methods and results found in the book cited above. However, we have made a rule of referring to it only for technical assistance, and of repeating every definition needed for the comprehension of the present text.

Edition details

• Publisher: Princeton University Press
• Publication date: 1994
• Language: English
• ISBN 10: 069102992X
• ISBN 13: 9780691029924
• Binding: Paperback
• Number of pages: 398