Extensions of Rings of Holomorphic Functions.
Factorization of uniformly holomorphic functions
Let E be a complex Hausdorff locally convex space such that the strong dual E’ of E is sequentially complete, let F be a closed linear subspace of E and let U be a uniformly open subset of E. We denote by Π: E → E/F the canonical quotient mapping. In §1 we study the factorization of uniformly holomorphic functions through π. In §2 we study F-quotients of uniform type and introduce the concept of envelope of uF-holomorphy of a connected uniformly open subset U of E. The main result states that the...
Families of analytic discs in with boundaries on a prescribed submanifold
Fortsetzbarkeit k-analytischer Mengen.
Fortsetzbarkeit k-meromorpher Funktionen.
Fortsetzung von kohärenten analytischen Modulgarben.
Fourier and Poisson transformation associated to a semisimple Symmetrie space.
Functional calculus and the Gelfand transformation
Geometric regularity versus analytic regularity higher codimensional case
Geometry of hypersurfaces and mapping theorems in Cn.
Geometry of nuclear spaces. II - Linear topological invariants
Germs of holomorphic mappings between real algebraic hypersurfaces
We study germs of holomorphic mappings between general algebraic hypersurfaces. Our main result is the following. If and are two germs of real algebraic hypersurfaces in , , is not Levi-flat and is a germ at of a holomorphic mapping such that and then the so-called reflection function associated to is always holomorphic algebraic. As a consequence, we obtain that if is given in the so-called normal form, the transversal component of is always algebraic. Another corollary of...
Global time estimates for solutions to equations of dissipative type
Global time estimates of norms of solutions to general strictly hyperbolic partial differential equations are considered. The case of special interest in this paper are equations exhibiting the dissipative behaviour. Results are applied to discuss time decay estimates for Fokker-Planck equations and for wave type equations with negative mass.
Graphs with multiple sheeted pluripolar hulls
We study the pluripolar hulls of analytic sets. In particular, we show that hulls of graphs of analytic functions can be multiple sheeted and sheets can be separated by a set of zero dimension.
Group actions and envelopes of holomorphy.
Growth Properties of Pseudo-Convex Domains and Domains of Holomorphy in Locally Convex Topological Vector Spaces.
Hartogs extension phenomena for analytic curves.
Hartog's phenomenon for polyregular functions and projective dimension of related modules over a polynomial ring
In this paper we prove that the projective dimension of is , where is the ring of polynomials in variables with complex coefficients, and is the module generated by the columns of a matrix which arises as the Fourier transform of the matrix of differential operators associated with the regularity condition for a function of quaternionic variables. As a corollary we show that the sheaf of regular functions has flabby dimension , and we prove a cohomology vanishing theorem for open...
Hartogs type extension theorems on some domains in Kähler manifolds
Given a locally pseudoconvex bounded domain Ω, in a complex manifold M, the Hartogs type extension theorem is said to hold on Ω if there exists an arbitrarily large compact subset K of Ω such that every holomorphic function on Ω-K is extendible to a holomorphic function on Ω. It will be reported, based on still unpublished papers of the author, that the Hartogs type extension theorem holds in the following two cases: 1) M is Kähler and ∂Ω is C²-smooth and not Levi flat; 2) M is compact Kähler and...
Holomorphe Korrespondenzen und meromorphe Abbildungen allgemeiner komplexer Räume.