Interpolating sequences of complex hyperplanes in the unit ball of ${\mathbb {C}}^n$

Pascal J. Thomas

Displaying similar documents to “Interpolating sequences of complex hyperplanes in the unit ball of $ℂ^{n}$ ”

Interpolation by holomorphic functions in the unit ball with polynomial growth

Xavier Massaneda (1997)

Annales de la Faculté des sciences de Toulouse : Mathématiques

Similarity:

Universal divisors in Hardy spaces

E. Amar, C. Menini (2000)

Studia Mathematica

Similarity:

We study a division problem in the Hardy classes $H^{p} ()$ of the unit ball of $ℂ^{2}$ which generalizes the $H^{p}$ corona problem, the generators being allowed to have common zeros. MPrecisely, if S is a subset of , we study conditions on a $ℂ^{k}$ -valued bounded Mholomorphic function B, with $B_{| S} = 0$ , in order that for 1 ≤ p < ∞ and any function $f \in H^{p} ()$ with $f_{| S} = 0$ there is a $ℂ^{k}$ -valued $H^{p} ()$ holomorphic function F with f = B·F, i.e. the module generated by the components of B in the Hardy class $H^{p} ()$ is the entire module $M_{S} : = f \in H^{p} () : f_{| S} = 0$ . As a...

Polydisc slicing in $ℂ^{n}$

Krzysztof Oleszkiewicz, Aleksander Pełczyński (2000)

Studia Mathematica

Similarity:

Let D be the unit disc in the complex plane ℂ. Then for every complex linear subspace H in $ℂ^{n}$ of codimension 1, $v o l_{2 n - 2} (D^{n - 1}) \leq v o l_{2 n - 2} (H \cap D^{n}) \leq 2 v o l_{2 n - 2} (D^{n - 1})$ . The lower bound is attained if and only if H is orthogonal to the versor $e_{j}$ of the jth coordinate axis for some j = 1,...,n; the upper bound is attained if and only if H is orthogonal to a vector $e_{j} + σ e_{k}$ for some 1 ≤ j < k ≤ n and some σ ∈ ℂ with |σ| = 1. We identify $ℂ^{n}$ with $ℝ^{2 n}$ ; by $v o l_{k} (\cdot)$ we denote the usual k-dimensional volume in $ℝ^{2 n}$ . The result is a complex counterpart of Ball’s [B1]...

Disks extremal with respect to interpolation constants.

Nguyen Van Trao (2000)

Publicacions Matemàtiques

Similarity:

We define a function μ from the set of sequences in the unit ball to R* by taking the greatest lower bound of the reciprocal of the interpolating constant of the sequences of the disk which get mapped to the given sequence by a holomorphic mapping from the disk to the ball. Its properties are studied in the spirit of the work of Amar and Thomas.

Ahlfors’ currents in higher dimension

Henry de Thélin (2010)

Annales de la faculté des sciences de Toulouse Mathématiques

Similarity:

We consider a nondegenerate holomorphic map $f : V \mapsto X$ where $(X, ω)$ is a compact Hermitian manifold of dimension larger than or equal to $k$ and $V$ is an open connected complex manifold of dimension $k$ . In this article we give criteria which permit to construct Ahlfors’ currents in $X$ .

Concentration and flatness properties of the singular set of bisected balls

Francesco Maddalena, Sergio Solimini (2001)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Similarity:

A new estimate for the sum $M (x) = \sum_{n \leq x} μ (n)$

R. MacLeod (1967)

Acta Arithmetica

Similarity:

A maximum principle for the Bergman space.

Boris Korenblum (1991)

Publicacions Matemàtiques

Similarity:

Let f(z) and g(z) be holomorphic in the open unit disk D and let Z_f and Z_g be their zero sets. If Z_f ⊃ Z_g and |f(z)| ≥ |g(z)| (1/2 e^-2 < |z| < 1), then || f || ≥ || g || where || · || is the Bergman norm: || f ||² = π^-1 ∫_D |f(z)|² dm (dm is the Lebesgue area measure).

Displaying similar documents to “Interpolating sequences of complex hyperplanes in the unit ball of ℂ n ”

Displaying similar documents to “Interpolating sequences of complex hyperplanes in the unit ball of $ℂ^{n}$ ”