L2 estimates and existence theorems for the ∂ operator

1965/01/01 by Lars Hörmander · 13 citations
Mathematics · #Advanced Harmonic Analysis Research #Numerical methods in inverse problems #Differential Equations and Boundary Problems

paper · pdf · doi:10.1007/bf02391775

openalex publication_date 1965/01/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/10

Abstract

The theory of analytic function of several complex variables, as presented for example in the Cartan seminars First one only studies functions in polycylinders (products of open sets in the different coordinate planes). The extension of the results to more general domains is then achieved by embedding them as submanifolds of polycylinders in spaces of high dimension. The success of this procedure depends of course on the invariance of

Citations

• The Analytic Embedding of Abstract Real-Analytic Manifolds
• �ber die �quivalenz der pseudokonvexen Gebiete und der Holomorphiegebiete im Raum vonn komplexen Ver�nderlichen
• Sur les fonctionnelles analytiques et la transformation de Fourier-Borel
• Sur les fonctions analytiques de plusieurs variables

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• The Index theorem for quasi-tori
• Bergman theory of certain generalized Hartogs triangles
• Curvature restrictions for Levi-flat real hypersurfaces in complex projective planes
• Boundary behavior of the Szegö kernel
• The Closed Range Property for the ∂ -Operator on Planar Domains
• Bergman kernel and complex singularity exponent
• Positive factorizations of pseudoperiodic homeomorphisms
• Function of several complex variables [wikipedia]