An analog of the Stolz Angle for the unit ball in {$\mathbb{C}^n$}

Abstract

By a (ρ, c, q)-wedge in the unit ball {$\mathbb{B}^n \subset \mathbb{C}^n$} we mean the union of the sets {$\mathbb{B}_\rho ^n$} and E_c,q(e₀), where {$\mathbb{B}_\rho ^n = \left\{ {z \in \mathbb{C}^n :\left| z \right| \leqslant \rho } \right\}$}, 0<ρ<1, |e₀|=1, 0<q<1, {$\rho > 1 - \frac{{\left( {1 - q} \right)^2 }}{{2\left( {1 + c^2 } \right)}}$}, and {$E_{c,q} \left( {e_0 } \right) = \left\{ {z \in \mathbb{B}^n :\left| {Im\left( {1 - \left( {z,e_0 } \right)} \right)} \right| \leqslant c{\text{ Re}}\left( {{\text{1 - }}\left( {{\text{z,}}e_0 } \right)} \right);\left| z \right|^2 - \left| {\left( {z,e_0 } \right)} \right|^2 \leqslant q\left( {1 - \left| {\left( {z,e_0 } \right)} \right|^2 } \right)} \right\}$} (here (z,χ) is the usual scalar product in {$\mathbb{C}^n$}). We denote by T_a, {${\rm T}_a$}, a≠0, the intersection of {$\mathbb{B}^n$} and the hyperplane {z:(z, a)=|a|²}. This paper contains a description of the sets Z of the form {$\bigcup\limits_{a \in A} { {\rm T}_\alpha }$}, where A belongs to a finite union of (ρ, c, q)-wedges with 0<q<1/2. These sets may occur as zero-sets or interpolation set for functions belonging to {$H^\infty \left( {\mathbb{B}^n } \right)$}. Bibliography: 9 titles.