TY - JOUR

T1 - An analog of the stolz angle for the unit ball in ℂn

AU - Shirokov, N. A.

PY - 2000

Y1 - 2000

N2 - By a (ρ, c, q)-wedge in the unit ball double-struck B signn ⊂ ℂn we mean the union of the sets double-struck B sign ρn and Ec, q(e0), where double-struck B signρ n = (z ∈ ℂn: z ≤ ρ), 0 < ρ < 1, e0 = 1, 0 < q < 1, ρ > 1 - (1-q)2, and Ec, q(e0) = (z ∈ double-struck B signn: Im(1 - (z, e0)) ≤ cRe(1 - (z, e0)); z2 - (z, e0)2 ≤ q(1 - (z, e0)2)) (here (z, ξ) is the usual scalar product in ℂn). We denote by Ta, a ∈ double-struck B signn, a ≠ 0, the intersection double-struck B signn and the hyperplane (z: (z, a) = a2). This paper contains a description of the sets Z of the form ∪a∈A Ta, 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 sets for functions belonging to H∞ (double-struck B signn).

AB - By a (ρ, c, q)-wedge in the unit ball double-struck B signn ⊂ ℂn we mean the union of the sets double-struck B sign ρn and Ec, q(e0), where double-struck B signρ n = (z ∈ ℂn: z ≤ ρ), 0 < ρ < 1, e0 = 1, 0 < q < 1, ρ > 1 - (1-q)2, and Ec, q(e0) = (z ∈ double-struck B signn: Im(1 - (z, e0)) ≤ cRe(1 - (z, e0)); z2 - (z, e0)2 ≤ q(1 - (z, e0)2)) (here (z, ξ) is the usual scalar product in ℂn). We denote by Ta, a ∈ double-struck B signn, a ≠ 0, the intersection double-struck B signn and the hyperplane (z: (z, a) = a2). This paper contains a description of the sets Z of the form ∪a∈A Ta, 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 sets for functions belonging to H∞ (double-struck B signn).

UR - http://www.scopus.com/inward/record.url?scp=52849121485&partnerID=8YFLogxK

U2 - 10.1007/BF02673746

DO - 10.1007/BF02673746

M3 - Article

AN - SCOPUS:52849121485

VL - 101

SP - 3216

EP - 3229

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 3

ER -