Hyperfunctions on Hypo-Analytic Manifolds (eBook)

Paulo D. Cordaro, François Treves (Autoren)

eBook Download: PDF

2016
Princeton University Press (Verlag)
978-1-4008-8256-4 (ISBN)

Infos

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.

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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.

Produkt-Details

• Erscheint lt. Verlag: 2.3.2016
• Reihe/Serie: Annals of Mathematics Studies
• Reihe/Serie: Annals of Mathematics Studies
• Verlagsort: Princeton
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
• Schlagworte: Alexander Grothendieck • analytic function • Analytic manifold • Borel transform • Boundary value problem • bounded function • Bounded set • Bounded set (topological vector space) • C0 • Cauchy problem • Codimension • coefficient • cohomology • Compact space • complex manifold • complex number • Complex Space • Connected space • continuous function • Continuous function (set theory) • convex set • convolution • cotangent bundle • counterexample • CR manifold • Dense set • de Rham cohomology • Differential operator • Disjoint union • Domain of a function • Eigenvalues and Eigenvectors • Embedding • Entire function • Equation • equivalence class • equivalence relation • Euclidean space • existential quantification • Exterior algebra • exterior derivative • fiber bundle • Fourier transform • Functional Analysis • function space • fundamental solution • Harmonic function • holomorphic function • Homomorphism • hyperfunction • hypersurface • Infimum and supremum • Integration by parts • Laplace's equation • Limit of a sequence • Linear map • Linear space (geometry) • Linear subspace • Locally convex topological vector space • Mathematical Induction • Montel space • Montel's theorem • Morphism • Neighbourhood (mathematics) • Norm (mathematics) • Open set • partial derivative • partial differential equation • Polytope • Presheaf (category theory) • pullback • Pullback (category theory) • Quotient space (topology) • Radon measure • Real structure • Riemann sphere • Serre Duality • Several Complex Variables • sheaf cohomology • Sheaf (mathematics) • Singular integral • Sobolev Space • Special case • submanifold • subsequence • Subset • Summation • tangent bundle • Theorem • Topology • Topology of uniform convergence • Transitive relation • transpose • Transversal (geometry) • uniform convergence • uniqueness theorem • Vanish at infinity • Variable (mathematics) • vector bundle • Vector field • wave front set
• ISBN-10: 1-4008-8256-7 / 1400882567
• ISBN-13: 978-1-4008-8256-4 / 9781400882564