Hyperfunctions on Hypo-Analytic Manifolds

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.

Info autore

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.

Riassunto

Helps reader 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. This book provides definitions of the hypo-analytic wave-front set and of the Fourier-Bros-Iagolnitzer transform of a hyperfunction.

Dettagli sul prodotto

• Autori: Paulo D. Cordaro, Michael Armstrong, Paulo D. Coraro, PICKETT, Paulo Cordaro, Francois Treves, François Treves, Cordaro Paulo, Cordaro Paulo D.
• Con la collaborazione di: Elias Cordaro (Editore), Francois Mather (Editore), Phillip Griffiths (Editore)
• Editore: University Presses
• Contenuto: Libro
• Forma del prodotto: Tascabile
• Data pubblicazione: 23.10.1994
• Categoria: Scienze naturali, medicina, informatica, tecnica > Matematica > Geometria
• EAN: 9780691029924
• ISBN: 978-0-691-02992-4
• Numero di pagine: 378
• Dimensioni (della confezione): 19.7 x 25.4 cm
• Peso (della confezione): 539 g
• Serie: Annals of Mathematics Studies > 0136; Annals of Mathematics Studies
• Categorie: MATHEMATICS / Geometry / General, MATHEMATICS / Topology, geometry, Homomorphism, Theorem, Topology, equation, Embedding, Function space, Partial differential equation, Boundary value problem, cohomology, submanifold, vector bundle, Fourier transform, differential operator, tangent bundle, Cauchy problem, Sobolev space, Riemann sphere, fiber bundle, convolution, compact space, holomorphic function, mathematical induction, Complex manifold, Complex space, wave front set, de Rham cohomology, Vector field, analytic function, special case, uniqueness theorem, Eigenvalues and Eigenvectors, Harmonic Function, Variable (mathematics), Complex number, Partial derivative, Summation, Transitive relation, Open set, Sheaf (mathematics), Linear Map, Existential quantification, Hypersurface, C0, Presheaf (category theory), Norm (mathematics), Continuous function (set theory), Bounded set (topological vector space), Pullback (category theory), Infimum and supremum, Integration by parts, Quotient space (topology), Exterior derivative, Transversal (geometry), Topology of uniform convergence, Singular integral, Linear space (geometry), Laplace's equation, Linear subspace, Montel space, Neighbourhood (mathematics), several complex variables, Hyperfunction, Borel transform, Radon measure, Montel's theorem, Analytic manifold, Exterior algebra, Serre duality, CR manifold, sheaf cohomology