Orthogonal testing families and holomorphic extension from the sphere to the ball

2018/08/22 by Luca Baracco, Baracco, Luca, Martino Fassina +1
Mathematics · #32V20 #32V25 (Primary) #32V40 (Secondary) #Complex Variables (math.CV) #FOS: Mathematics #math.CV #msc:32V20 #msc:32V25 #msc:32V40

paper · pdf · doi:10.48550/arxiv.1808.07444

9 pages, 2 figures. Final version to appear in Math. Z

arxiv created 2019/01/16 · arxiv updated 2019/01/17

Abstract

Let \mathbbB² denote the open unit ball in ℂ², and let p∈ ℂ²∖\mathbbB². We prove that if f is an analytic function on the sphere ∂\mathbbB² that extends holomorphically in each variable separately and along each complex line through p, then f is the trace of a holomorphic function in the ball.

Related

• Separate holomorphic extension along lines and holomorphic extension from the sphere to the ball
• Small families of complex lines for testing holomorphic extendibility
• Testing families of analytic discs in the unit ball
• Boundary Traces of Holomorphic Functions on the Unit Ball in ℂⁿ
• Meromorphic extensions from small families of circles and holomorphic extensions from spheres