Holomorphic equivariant cohomology.
Holomorphic extension from the sphere to the ball in Hilbert space
Holomorphic extension from weakly pseudoconcave CR manifolds
Holomorphic extension maps for spaces of Whitney jets.
The key result (Theorem 1) provides the existence of a holomorphic approximation map for some space of C∞-functions on an open subset of Rn. This leads to results about the existence of a continuous linear extension map from the space of the Whitney jets on a closed subset F of Rn into a space of holomorphic functions on an open subset D of Cn such that D ∩ Rn = RnF.
Holomorphic extension of generalizations of functions.
Holomorphic extension of generalizations of functions. II.
Holomorphic extension to open hulls
Holomorphic extensions of formal objects
We are interested on families of formal power series in parameterized by (). If every is a polynomial whose degree is bounded by a linear function ( for some and ) then the family is either convergent or the series for all except a pluri-polar set. Generalizations of these results are provided for formal objects associated to germs of diffeomorphism (formal power series, formal meromorphic functions, etc.). We are interested on describing the nature of the set of parameters where...
Holomorphic Families of Open Riemann Surfaces.
Holomorphic Fiber Bundles whose Fibers are Bounded Stein Domains with Zero First Betti Number.
Holomorphic Fibrations of Bounded Domains.
Holomorphic flows and complex structures on products of odd dimensional spheres.
Holomorphic foliations by curves on with non-isolated singularities
Let be a holomorphic foliation by curves on . We treat the case where the set consists of disjoint regular curves and some isolated points outside of them. In this situation, using Baum-Bott’s formula and Porteuos’theorem, we determine the number of isolated singularities, counted with multiplicities, in terms of the degree of , the multiplicity of along the curves and the degree and genus of the curves.
Holomorphic framings for projections in a Banach algebra.
Holomorphic functions and Banach-nuclear decompositions of Fréchet spaces
We introduce a decomposition of holomorphic functions on Fréchet spaces which reduces to the Taylor series expansion in the case of Banach spaces and to the monomial expansion in the case of Fréchet nuclear spaces with basis. We apply this decomposition to obtain examples of Fréchet spaces E for which the τ_{ω} and τ_{δ} topologies on H(E) coincide. Our result includes, with simplified proofs, the main known results-Banach spaces with an unconditional basis and Fréchet nuclear spaces with DN [2,...
Holomorphic functions and subelliptic heat kernels over Lie groups
Holomorphic functions of fast growth on submanifolds of the domain
We construct a function f holomorphic in a balanced domain D in such that for every positive-dimensional subspace Π of , and for every p with 1 ≤ p < ∞, is not -integrable on Π ∩ D.
Holomorphic functions on Fréchet spaces with Schauder basis.
Holomorphic functions on locally convex topological vector spaces. II. Pseudo convex domains
In this article we discuss the relationship between domains of existence domains of holomorphy, holomorphically convex domains, pseudo convex domains, in the context of locally convex topological vector spaces. By using the method of Hirschowitz for and the method used for Banach spaces with a basis we prove generalisations of the Cartan-Thullen-Oka-Norguet-Bremmerman theorem for finitely polynomially convex domains in a variety of locally convex spaces which include the following:1) -projective...
Holomorphic functions with singularities on algebraic sets.