Leseprobe
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Hyperfunctions on Hypo-Analytic Manifolds (AM-136), Volume 136
François Treves, Paulo Cordaro
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Naturwissenschaften, Medizin, Informatik, Technik / Mathematik
Beschreibung
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.
Kundenbewertungen
Linear space (geometry), Norm (mathematics), Partial derivative, Cauchy problem, Transversal (geometry), Montel's theorem, Linear subspace, CR manifold, Continuous function (set theory), Singular integral, Variable (mathematics), Complex number, Open set, Exterior derivative, Laplace's equation, Hypersurface, Theorem, Uniqueness theorem, Submanifold, Infimum and supremum, Partial differential equation, Exterior algebra, Sheaf (mathematics), Embedding, Hyperfunction, Topology of uniform convergence, Neighbourhood (mathematics), Analytic manifold, Bounded set (topological vector space), Differential operator, Homomorphism, Linear map, Transitive relation, Harmonic function, Sheaf cohomology, Quotient space (topology), Cohomology, Radon measure, De Rham cohomology, Holomorphic function, Presheaf (category theory), Existential quantification, Fiber bundle, Tangent bundle, Convolution, C0, Eigenvalues and eigenvectors, Vector field, Summation, Sobolev space, Montel space, Pullback (category theory), Vector bundle, Several complex variables, Integration by parts, Topology, Riemann sphere, Analytic function, Complex space, Serre duality, Special case, Mathematical induction, Equation, Compact space, Fourier transform, Complex manifold, Function space, Borel transform, Wave front set, Boundary value problem