Hyperfunctions on Hypo-Analytic Manifolds (AM-136), Volume 136 / / Paulo Cordaro, François Treves

• Autore: Cordaro Paulo
• Pubblicazione: Princeton, NJ : , : Princeton University Press, , [2016]; ©1995
• Descrizione fisica: 1 online resource (398 pages)
• Disciplina: 515/.782
• Soggetto topico: Hyperfunctions; Submanifolds
• Soggetto non controllato: Alexander Grothendieck; Analytic function; Analytic manifold; Borel transform; Boundary value problem; Bounded function; Bounded set (topological vector space); Bounded set; C0; CR manifold; Cauchy problem; Codimension; Coefficient; Cohomology; Compact space; Complex manifold; Complex number; Complex space; Connected space; Continuous function (set theory); Continuous function; Convex set; Convolution; Cotangent bundle; Counterexample; De Rham cohomology; Dense set; 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; Function space; Functional analysis; 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 (category theory); Pullback; Quotient space (topology); Radon measure; Real structure; Riemann sphere; Serre duality; Several complex variables; Sheaf (mathematics); Sheaf cohomology; Singular integral; Sobolev space; Special case; Submanifold; Subsequence; Subset; Summation; Tangent bundle; Theorem; Topology of uniform convergence; Topology; Transitive relation; Transpose; Transversal (geometry); Uniform convergence; Uniqueness theorem; Vanish at infinity; Variable (mathematics); Vector bundle; Vector field; Wave front set
• Persona (resp. second.): TrevesFrançois
• Note generali: Bibliographic Level Mode of Issuance: Monograph
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: Frontmatter -- CONTENTS -- PREFACE -- 0.1 BACKGROUND ON SHEAVES OF VECTOR SPACES OVER A MANIFOLD -- 0.2 BACKGROUND ON SHEAF COHOMOLOGY -- CHAPTER I. HYPERFUNCTION S IN A MAXIMAL HYPO-ANALYTIC STRUCTURE -- CHAPTER II. MICROLOCAL THEORY OF HYPERFUNCTIONS ON A MAXIMALLY REAL SUBMANIFOLD OF COMPLEX SPACE -- CHAPTER III. HYPERFUNCTION SOLUTIONS IN A HYPO-ANALYTIC MANIFOLD -- CHAPTER IV. TRANSVERSAL SMOOTHNESS OF HYPERFUNCTION SOLUTIONS -- HISTORICAL NOTES -- BIBLIOGRAPHICAL REFERENCES -- INDEX OF TERMS
• Sommario/riassunto: 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.
• Titolo autorizzato: Hyperfunctions on Hypo-Analytic Manifolds (AM-136), Volume 136
• ISBN: 1-4008-8256-7
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910154744403321
• Lo trovi qui: Univ. Federico II
• Serie: Annals of mathematics studies ; ; no. 136.