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We define a class of spaces $H_{μ}^{p}$ , 0 < p < ∞, of holomorphic functions on the tube, with a norm of Hardy type: ${| | F | |}_{H_{μ}^{p}}^{p} = s u p_{y \in Ω} \int_{Ω ̅} \int_{ℝ ⁿ} {| F (x + i (y + t)) |}^{p} d x d μ (t)$ . 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 $H_{μ}^{p}$ , and when p ≥ 1, characterize the boundary values as the functions in $L_{μ}^{p}$ 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

C. Andrade, L. Loura (2009)

Mathematica Bohemica

In this paper we define, by duality methods, a space of ultradistributions $_{ω}^{'} (ℝ^{N})$ . 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 $𝔾_{ω}^{'} (ℝ^{N})$ 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

Maciej Klimek, Marta Kosek (2009)

Annales Polonici Mathematici

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 $L^{p}$ -norm.

Harfaoui, Mohammed (2010)

International Journal of Mathematics and Mathematical Sciences

Generic subgroups of Aut $𝔹^{n}$

Chiara de Fabritiis (2002)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

We prove that for a parabolic subgroup $Γ$ of $Aut 𝔹^{n}$ the fixed points sets of all elements in $Γ ∖ {{id}_{𝔹^{n}}}$ are the same. This result, together with a deep study of the structure of subgroups of $Aut 𝔹^{n}$ acting freely and properly discontinuously on $𝔹^{n}$ , entails a generalization of the so called weak Hurwitz’s theorem: namely that, given a complex manifold $X$ covered by $𝔹^{n}$ and such that the group of deck transformations of the covering is “sufficiently generic”, then ${id}_{X}$ is isolated in $Hol (X, X)$ .

Geometric regularity versus analytic regularity higher codimensional case

E. Amar, L. Lempert (1990)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Geometric regularity versus functional regularity

E. Amar (1987)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Geometry and function algebra on pseudo-flat manifolds

A. Milani, C. Rea (1972)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Geometry of nuclear spaces. III - Spaces of holomorphic functions

B. Mityagin (1978/1979)

Séminaire Analyse fonctionnelle (dit "Maurey-Schwartz")

Geometry of the locus of polynomials of degree 4 with iterative roots

Beata Strycharz-Szemberg, Tomasz Szemberg (2011)

Open Mathematics

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 $\bar{\partial}$ -equation on Stein manifolds

Gennadi M. Henkin, Jürgen Leiterer (1981)

Annales Polonici Mathematici

Global regularity of the ...-Neumann problem on circular domains.

So-Chin Chen (1989)

Mathematische Annalen

Good-irreducible inner functions on a polydisc

Eric T. Sawyer (1979)

Annales de l'institut Fourier

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.

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