General Cauchy formulas in
Generalization of results about the Bohr radius for power series
The Bohr radius for power series of holomorphic functions mapping Reinhardt domains 𝓓 ⊂ ℂⁿ into a convex domain G ⊂ ℂ is independent of the domain G.
Generalizations of inequalities of Littlewood and Paley.
Generalized Dirichlet series and -functions
Generalized Hardy spaces on tube domains over cones
We define a class of spaces , 0 < p < ∞, of holomorphic functions on the tube, with a norm of Hardy type: . We allow μ to be any quasi-invariant measure with respect to a group acting simply transitively on the cone. We show the existence of boundary limits for functions in , and when p ≥ 1, characterize the boundary values as the functions in satisfying the tangential CR equations. A careful description of the measures μ when their supports lie on the boundary of the cone is also provided....
Generalized Hermitean ultradistributions
In this paper we define, by duality methods, a space of ultradistributions . This space contains all tempered distributions and is closed under derivatives, complex translations and Fourier transform. Moreover, it contains some multipole series and all entire functions of order less than two. The method used to construct led us to a detailed study, presented at the beginning of the paper, of the duals of infinite dimensional locally convex spaces that are inductive limits of finite dimensional...
Generalized iterated function systems, multifunctions and Cantor sets
Using a construction similar to an iterated function system, but with functions changing at each step of iteration, we provide a natural example of a continuous one-parameter family of holomorphic functions of infinitely many variables. This family is parametrized by the compact space of positive integer sequences of prescribed growth and hence it can also be viewed as a parametric description of a trivial analytic multifunction.
Generalized order and best approximation of entire function in -norm.
Generic subgroups of Aut
We prove that for a parabolic subgroup of the fixed points sets of all elements in are the same. This result, together with a deep study of the structure of subgroups of acting freely and properly discontinuously on , entails a generalization of the so called weak Hurwitz’s theorem: namely that, given a complex manifold covered by and such that the group of deck transformations of the covering is “sufficiently generic”, then is isolated in .
Geometric regularity versus analytic regularity higher codimensional case
Geometric regularity versus functional regularity
Geometry and function algebra on pseudo-flat manifolds
Geometry of nuclear spaces. III - Spaces of holomorphic functions
Geometry of the locus of polynomials of degree 4 with iterative roots
We study polynomial iterative roots of polynomials and describe the locus of complex polynomials of degree 4 admitting a polynomial iterative square root.
Global integral formulas for solving the -equation on Stein manifolds
Global regularity of the ...-Neumann problem on circular domains.
Good-irreducible inner functions on a polydisc
An explicit formula is developed for Nevanlinna class functions whose behaviour at the boundary is “sufficiently rational” and is then used to deduce the uniqueness of the factorization of such inner functions. A generalization of a theorem of Frostman is given and the above results are then applied to the construction of good and/or irreducible inner functions on a polydisc.
Gradients des fonctions intérieures dans la boule unité de ...n.
Group actions and envelopes of holomorphy.
Growth of functions in tubes.