Hyperfunctions on Hypo-Analytic Manifolds (AM-136)
Paulo D. Cordaro & François Treves

Paper | 1994 | $79.00 / £55.00
378 pp. | 6 x 9

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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.

Table of Contents:

• 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

Series:

• Annals of Mathematics Studies
  Phillip A. Griffiths, John N. Mather, and Elias M. Stein, Editors

Subject Area:

• Mathematics

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For customers in the U.S., Canada, Latin America, Asia, and Australia
Paper: $79.00 ISBN13: 978-0-691-02992-4

For customers in Europe, Africa, the Middle East, and India
Paper: £55.00 ISBN13: 978-0-691-02992-4

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