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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 $Hol (X, X)$ .

Growth properties of entire functions depending on a parameter

Stefan Halvarsson (1996)

Annales Polonici Mathematici

We study the growth of parameter-dependent entire functions. We are mainly interested in the case where the functions depend holomorphically on the parameter.

Hinfty + LE in several variables.

Julià Cufi (1982)

Collectanea Mathematica

Holomorphic functions of fast growth on submanifolds of the domain

Piotr Jakóbczak (1998)

Annales Polonici Mathematici

We construct a function f holomorphic in a balanced domain D in $ℂ^{N}$ such that for every positive-dimensional subspace Π of $ℂ^{N}$ , and for every p with 1 ≤ p < ∞, ${f |}_{Π \cap D}$ is not $L^{p}$ -integrable on Π ∩ D.

Holomorphic functions with singularities on algebraic sets.

Sičiak, Józef (2001)

Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Universitatis Iagellonicae Acta Mathematica

Holomorphic Lipschitz functions in balls.

Walter Rudin (1978)

Commentarii mathematici Helvetici

Holomorphic Mappings from the Ball and Polydisc.

H. Alexander (1974)

Mathematische Annalen

Holomorphic Sobolev spaces on the ball [Book]

Frank Beatrous, Jacob Burbea (1989)

Identity surfaces.

Tutschke, W. (2000)

Zeitschrift für Analysis und ihre Anwendungen

Inner Functions and Boundary Values in H... (...) and A (...) in Smoothly Bounded Pseudoconvex Domains.

Erik Low (1984)

Mathematische Zeitschrift

Integral Formulas for the ... ....-Equation and Zeros of Bounded Holomorphic Functions in the Unit Ball.

Bo Berndtsson (1980)

Mathematische Annalen

Integral representation of $n$ -variable positive real functions

Jiří Gregor (1980)

Commentationes Mathematicae Universitatis Carolinae

Integral representations for some weighted classes of functions holomorphic in matrix domains

M. M. Djrbashian, A. H. Karapetyan (1991)

Annales Polonici Mathematici

In 1945 the first author introduced the classes $H^{p} (α)$ , 1 ≤ p<∞, α > -1, of holomorphic functions in the unit disk with finite integral (1) ∬ |f(ζ)|p (1-|ζ|²)α dξ dη < ∞ (ζ=ξ+iη) and established the following integral formula for $f \in H^{p} (α)$ : (2) f(z) = (α+1)/π ∬ f(ζ) ((1-|ζ|²)α)/((1-zζ̅)2+α) dξdη, z∈ . We have established that the analogues of the integral representation (2) hold for holomorphic functions in Ω from the classes $L^{p} (Ω; {[K (w)]}^{α} d m (w))$ , where: 1) $Ω = w = (w ₁, . . ., w_{n}) \in ℂ^{n} : I m w ₁ > \sum_{k = 2}^{n} | w_{k} | ²$ , $K (w) = I m w ₁ - \sum_{k = 2}^{n} | w_{k} | ²$ ; 2) Ω is the matrix domain consisting of those complex m...

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