Hyperfunctions on hypo-analytic manifolds
著者
書誌事項
Hyperfunctions on hypo-analytic manifolds
（Annals of mathematics studies, no. 136）
Princeton University Press, 1994
- : cloth
- : pbk
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注記
Includes bibliographical references (p. [365]-369) and index of terms
内容説明・目次
- 巻冊次
-
: pbk ISBN 9780691029924
内容説明
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.
目次
* 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
- 巻冊次
-
: cloth ISBN 9780691029931
内容説明
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.
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