Boundary Forelli theorem for the sphere in \mathbb Cⁿ and n+1 bundles of complex lines

2010/03/31 by Mark Agranovsky, Agranovsky, Mark
Mathematics · #32D #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #Meromorphic and Entire Functions #math.CV #msc:32D

paper · pdf · doi:10.48550/arxiv.1003.6125

arxiv created 2010/03/31 · openalex publication_date 2010/03/31 · arxiv updated 2010/04/01 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28

Abstract

Let Bⁿ be the unit ball in \mathbb Cⁿ and let the points a₁,...,a_n+1 ∈ Bⁿ are affinely independent. If f ∈ C(∂ Bⁿ) and for any complex line L, containing at least one of the points a_j, the restriction f|_{L ∩ ∂ Bⁿ} extends holomorphically in the disc L ∩ Bⁿ, then f is the boundary value of a holomorphic function in Bⁿ. The condition for the points a_j is sharp. The result confirms a conjecture from the preprint arXiv:0910.3592 by the author.

Related

• Boundary Traces of Holomorphic Functions on the Unit Ball in ℂⁿ
• On the generalization of Forelli's theorem
• Conjecture de Globevnik-Stout et theoreme de Morera pour une chaine holomorphe
• A boundary Schwarz Lemma for holomorphic mappings between unit balls of different dimensions
• Separate holomorphic extension along lines and holomorphic extension from the sphere to the ball