Hyperfunctions on Hypo-Analytic Manifolds
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A01=Francois Treves
A01=Paulo Cordaro
A01=Paulo D. Cordaro
Analytic function
Analytic manifold
Author_Francois Treves
Author_Paulo Cordaro
Author_Paulo D. Cordaro
Borel transform
Boundary value problem
Bounded set (topological vector space)
C0
Category=PBM
Category=PBP
Cauchy problem
Cohomology
Compact space
Complex manifold
Complex number
Complex space
Continuous function (set theory)
Convolution
CR manifold
De Rham cohomology
Differential operator
Eigenvalues and eigenvectors
Embedding
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Equation
Existential quantification
Exterior algebra
Exterior derivative
Fiber bundle
Fourier transform
Function space
Harmonic function
Holomorphic function
Homomorphism
Hyperfunction
Hypersurface
Infimum and supremum
Integration by parts
Laplace's equation
Linear map
Linear space (geometry)
Linear subspace
Mathematical induction
Montel space
Montel's theorem
Neighbourhood (mathematics)
Norm (mathematics)
Open set
Partial derivative
Partial differential equation
Presheaf (category theory)
Pullback (category theory)
Quotient space (topology)
Radon measure
Riemann sphere
Serre duality
Several complex variables
Sheaf (mathematics)
Sheaf cohomology
Singular integral
Sobolev space
Special case
Submanifold
Summation
Tangent bundle
Theorem
Topology
Topology of uniform convergence
Transitive relation
Transversal (geometry)
Uniqueness theorem
Variable (mathematics)
Vector bundle
Vector field
Wave front set
Product details
- ISBN 9780691029924
- Weight: 539g
- Dimensions: 197 x 254mm
- Publication Date: 23 Oct 1994
- Publisher: Princeton University Press
- Publication City/Country: US
- Product Form: Paperback
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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.
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.
