Analytic functionals and Bergman spaces
Analytic inversion of adjunction: extension theorems with gain
We establish new results on weighted -extension of holomorphic top forms with values in a holomorphic line bundle, from a smooth hypersurface cut out by a holomorphic function. The weights we use are determined by certain functions that we call denominators. We give a collection of examples of these denominators related to the divisor defined by the submanifold.
Application of the logarithmic differential to the holomorphic extension problem for -hyperfunctions.
Approximation polynomiale et extension holomorphe avec croissance sur une variété algébrique
We first give a general growth version of the theorem of Bernstein-Walsh-Siciak concerning the rate of convergence of the best polynomial approximation of holomorphic functions on a polynomially convex compact subset of an affine algebraic manifold. This can be considered as a quantitative version of the well known approximation theorem of Oka-Weil. Then we give two applications of this theorem. The first one is a generalization to several variables of Winiarski's theorem relating the growth of...
Balanced domains of holomorphy of type
Bases communes dans certains espaces de fonctions harmoniques et fonctions séparément harmoniques sur certains ensembles de
Bergman completeness of complete circular domains
Biholomorphic Mappings Between Certain Real Analytic Domains in C2.
Boundary Analyticity of Proper Holomorphic Maps of Domains with Non-Analytic Boundaries.
Boundary cross theorem in dimension 1
Let X, Y be two complex manifolds of dimension 1 which are countable at infinity, let D ⊂ X, G ⊂ Y be two open sets, let A (resp. B) be a subset of ∂D (resp. ∂G), and let W be the 2-fold cross ((D∪A)×B) ∪ (A×(B∪G)). Suppose in addition that D (resp. G) is Jordan-curve-like on A (resp. B) and that A and B are of positive length. We determine the "envelope of holomorphy" Ŵ of W in the sense that any function locally bounded on W, measurable on A × B, and separately holomorphic on (A × G) ∪ (D × B)...
Boundary Regularity of Proper Holomorphic Mappings.
Bounded holomorphic functions with multiple sheeted pluripolar hulls
We describe compact subsets K of ∂𝔻 and ℝ admitting holomorphic functions f with the domains of existence equal to ℂ∖K and such that the pluripolar hulls of their graphs are infinitely sheeted. The paper is motivated by a recent paper of Poletsky and Wiegerinck.
Carleman's formulas and conditions of analytic extendability
Cartan-Thullen theorem for domains spread over ...-spaces.
Cauchy-Kowalewski extension theorems and representations of analytic functionals acting over special classes of real n-dimensional submanifolds of
Cauchy-Riemann functions on manifolds of higher codimension in complex space.
Central morphisms and envelopes of holomorphy.
∂̅-cohomology and geometry of the boundary of pseudoconvex domains
In 1958, H. Grauert proved: If D is a strongly pseudoconvex domain in a complex manifold, then D is holomorphically convex. In contrast, various cases occur if the Levi form of the boundary of D is everywhere zero, i.e. if ∂D is Levi flat. A review is given of the results on the domains with Levi flat boundaries in recent decades. Related results on the domains with divisorial boundaries and generically strongly pseudoconvex domains are also presented. As for the methods, it is explained how Hartogs...
Complete Characterization of Holomorphic Chains of Codimension One.
Complete Hartogs Domains in C2 have Regular Bergman and Szegö Projections.