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200 10$aHyperfunctions on Hypo-Analytic Manifolds (AM-136), Volume 136 /$fPaulo Cordaro, François Treves
210  1$aPrinceton, NJ : $cPrinceton University Press, $d[2016]
210  4$dİ1995
215   $a1 online resource (398 pages)
225 0 $aAnnals of Mathematics Studies ;$v318
300   $aBibliographic Level Mode of Issuance: Monograph
311   $a0-691-02992-X 
311   $a0-691-02993-8 
320   $aIncludes bibliographical references and index.
327   $tFrontmatter -- $tCONTENTS -- $tPREFACE -- $t0.1 BACKGROUND ON SHEAVES OF VECTOR SPACES OVER A MANIFOLD -- $t0.2 BACKGROUND ON SHEAF COHOMOLOGY -- $tCHAPTER I. HYPERFUNCTION S IN A MAXIMAL HYPO-ANALYTIC STRUCTURE -- $tCHAPTER II. MICROLOCAL THEORY OF HYPERFUNCTIONS ON A MAXIMALLY REAL SUBMANIFOLD OF COMPLEX SPACE -- $tCHAPTER III. HYPERFUNCTION SOLUTIONS IN A HYPO-ANALYTIC MANIFOLD -- $tCHAPTER IV. TRANSVERSAL SMOOTHNESS OF HYPERFUNCTION SOLUTIONS -- $tHISTORICAL NOTES -- $tBIBLIOGRAPHICAL REFERENCES -- $tINDEX OF TERMS
330   $aIn the first two chapters of this book, the reader will find a complete and systematic exposition of the theory of hyperfunctions on totally real submanifolds of multidimensional complex space, in particular of hyperfunction theory in real space. The book provides precise definitions of the hypo-analytic wave-front set and of the Fourier-Bros-Iagolnitzer transform of a hyperfunction. These are used to prove a very general version of the famed Theorem of the Edge of the Wedge. The last two chapters define the hyperfunction solutions on a general (smooth) hypo-analytic manifold, of which particular examples are the real analytic manifolds and the embedded CR manifolds. The main results here are the invariance of the spaces of hyperfunction solutions and the transversal smoothness of every hyperfunction solution. From this follows the uniqueness of solutions in the Cauchy problem with initial data on a maximally real submanifold, and the fact that the support of any solution is the union of orbits of the structure.
410  0$aAnnals of mathematics studies ;$vno. 136.
606   $aHyperfunctions
606   $aSubmanifolds
610   $aAlexander Grothendieck.
610   $aAnalytic function.
610   $aAnalytic manifold.
610   $aBorel transform.
610   $aBoundary value problem.
610   $aBounded function.
610   $aBounded set (topological vector space).
610   $aBounded set.
610   $aC0.
610   $aCR manifold.
610   $aCauchy problem.
610   $aCodimension.
610   $aCoefficient.
610   $aCohomology.
610   $aCompact space.
610   $aComplex manifold.
610   $aComplex number.
610   $aComplex space.
610   $aConnected space.
610   $aContinuous function (set theory).
610   $aContinuous function.
610   $aConvex set.
610   $aConvolution.
610   $aCotangent bundle.
610   $aCounterexample.
610   $aDe Rham cohomology.
610   $aDense set.
610   $aDifferential operator.
610   $aDisjoint union.
610   $aDomain of a function.
610   $aEigenvalues and eigenvectors.
610   $aEmbedding.
610   $aEntire function.
610   $aEquation.
610   $aEquivalence class.
610   $aEquivalence relation.
610   $aEuclidean space.
610   $aExistential quantification.
610   $aExterior algebra.
610   $aExterior derivative.
610   $aFiber bundle.
610   $aFourier transform.
610   $aFunction space.
610   $aFunctional analysis.
610   $aFundamental solution.
610   $aHarmonic function.
610   $aHolomorphic function.
610   $aHomomorphism.
610   $aHyperfunction.
610   $aHypersurface.
610   $aInfimum and supremum.
610   $aIntegration by parts.
610   $aLaplace's equation.
610   $aLimit of a sequence.
610   $aLinear map.
610   $aLinear space (geometry).
610   $aLinear subspace.
610   $aLocally convex topological vector space.
610   $aMathematical induction.
610   $aMontel space.
610   $aMontel's theorem.
610   $aMorphism.
610   $aNeighbourhood (mathematics).
610   $aNorm (mathematics).
610   $aOpen set.
610   $aPartial derivative.
610   $aPartial differential equation.
610   $aPolytope.
610   $aPresheaf (category theory).
610   $aPullback (category theory).
610   $aPullback.
610   $aQuotient space (topology).
610   $aRadon measure.
610   $aReal structure.
610   $aRiemann sphere.
610   $aSerre duality.
610   $aSeveral complex variables.
610   $aSheaf (mathematics).
610   $aSheaf cohomology.
610   $aSingular integral.
610   $aSobolev space.
610   $aSpecial case.
610   $aSubmanifold.
610   $aSubsequence.
610   $aSubset.
610   $aSummation.
610   $aTangent bundle.
610   $aTheorem.
610   $aTopology of uniform convergence.
610   $aTopology.
610   $aTransitive relation.
610   $aTranspose.
610   $aTransversal (geometry).
610   $aUniform convergence.
610   $aUniqueness theorem.
610   $aVanish at infinity.
610   $aVariable (mathematics).
610   $aVector bundle.
610   $aVector field.
610   $aWave front set.
615  0$aHyperfunctions.
615  0$aSubmanifolds.
676   $a515/.782
700   $aCordaro$b Paulo, $01208527
702   $aTreves$b François, 
801  0$bDE-B1597
801  1$bDE-B1597
906   $aBOOK
912   $a9910154744403321
996   $aHyperfunctions on Hypo-Analytic Manifolds (AM-136), Volume 136$92788029
997   $aUNINA