Boundary Forelli conjecture for bundles of complex lines
Let be the unit ball, and let be vertices in general position. An -bundle of complex lines consists of the complex lines containing at least one of these vertices. Let be a continuous function on the unit sphere. For each such complex line , consider the restriction of to . Boundary Forelli conjecture. Any bundles of complex lines with vertices in general position test boundary values of holomorphic functions in : if holomorphically extends in every disc determined by these lines, then is the boundary value of a holomorphic function in . The conjecture identifies vertices lying in a hyperplane as the only obstruction to the continuous boundary version of the Forelli theorem; the supplied source does not indicate whether the conjecture has been resolved.
References
Primary source
Mark Agranovsky, “Boundary Forelli theorem for the sphere in C^n and n+1 bundles of complex lines”, arXiv:1003.6125 (2010).
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