Cordaro / Treves Hyperfunctions on Hypo-Analytic Manifolds

1. Auflage 2016
ISBN: 978-1-4008-8256-4
Verlag: De Gruyter
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 378 Seiten

Reihe: Annals of Mathematics Studies

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.

Autoren/Hrsg.

Cordaro, Paulo D.

Treves, François

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie Algebraische Geometrie

Inhaltsverzeichnis

- Hyperfunctions in a Maximal Hypo-Anayltic Structure

- Microlocal Theory of Hyperfunctions on a Maximally Real Submanifold of Complex Space

- Hyperfunction Solutions in a Hypo-Analytic Manifold

- Transversal Smoothness of Hyperfunction Solutions

Über Autor(innen)

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.