On the solvability of linear partial differential equations in spaces of hyperfunctions

DOI10.1007/BF02385666zbMath0910.46028OpenAlexW2093700143MaRDI QIDQ1127064

Paulo D. Cordaro, Jean-Marie Trepreau

Publication date: 5 November 1998

Published in: Arkiv för Matematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02385666

zbMATH Keywords

hyperfunctions on a maximal manifoldsystems of differential equations without compatibility conditions

Mathematics Subject Classification ID

Hyperfunctions, analytic functionals (46F15) Topological linear spaces of test functions, distributions and ultradistributions (46F05)

Related Items (5)

A new microlocal analysis of hyperfunctions ⋮ Principe de Hartogs dans les variétés CR. (The Hartogs principle for CR manifolds) ⋮ Global \(s\)-solvability and global \(s\)-hypoellipticity for certain perturbations of zero order of systems of constant real vector fields ⋮ Top-degree global solvability in CR and locally integrable hypocomplex structures ⋮ Hyperfunctions and (analytic) hypoellipticity

Cites Work

• Unnamed Item
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• Propagation of analyticity for a class of non-micro-characteristic operators
• Vanishing in highest degree for solutions of D-modules and perverse sheaves
• Sur le prolongement holomorphe des fonctions CR définies sur une hypersurface réelle de classe \(C^ 2\) dans \({\mathbb{C}}^ n\). (Holomorphic continuation of CR-functions defined on a real hypersurface of class \(C^ 2\) in \({\mathbb{C}}^ n)\)
• A property of the functions and distributions annihilated by a locally integrable system of complex vector fields
• On the reconstruction theorem of holonomic modules in the Gevrey classes
• On the maximally overdetermined system of linear differential equations. I
• Propagation of singularities and semi-global existence theorems for (pseudo-)differential operators of principal type
• On the \(C^ \infty\)-regularity of the \(\overline{\partial}\)-operator at the boundary of a domain in \(\mathbb{C}^ n\) whose Levi form has exactly \(s\) strictly negative eigenvalues
• Local solvability for \(\overline{\partial}\) with Gevrey regularity up to the boundary of a \(r\)- convex domain
• Necessary and sufficient conditions for the local solvability in hyperfunctions of a class of systems of complex vector fields
• Resolutions by hyperfunctions of sheaves of solutions of differential equations with constant coefficients
• Théorie des hyperfonctions
• On the existence and the regularity of solutions of linear pseudo- differential equations
• Holomorphic approximation and hyperfunction theory on a C\(^1\) totally real submanifold of a complex manifold
• On local solvability of linear partial differential equations
• Sur l'hypoellipticite analytique microlocale des operateurs de type principal
• Liouville's theorem and the maximum modulus principle for a system of complex vector fields
• On the Local Solvability for Top-Degree Forms in Hypo-Analytic Structures
• Orbits of Families of Vector Fields and Integrability of Distributions
• Solutions hyperfonctions des équations aux dérivées partielles du premier ordre
• On local solvability of linear partial differential equations part I: Necessary conditions
• The Theory of Hyperfunctions on Totally Real Subsets of a Complex Manifold with Applications to Extension Problems

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