Abstract
Let f ∈ C ω(∂B n), where B n is the unit ball of ℂn. We prove that if \(a,b \in {\overline B ^n}\), a ≠ b, for every complex line L passing through one of a or b, the restricted function \(f{|_{L \cap \partial {B^n}}}\) has a holomorphic extention to the cross-section L∩B n, then f is the boundary value of a holomorphic function in B n.
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This work was partially supported by the grant from ISF (Israel Science Foundation) 688/08. Some of this research was done as a part of European Science Foundation Networking Program HCAA.
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Agranovsky, M.L. Analog of a theorem of forelli for boundary values of holomorphic functions on the unit ball of ℂn . JAMA 113, 293–304 (2011). https://doi.org/10.1007/s11854-011-0008-9
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DOI: https://doi.org/10.1007/s11854-011-0008-9