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

Abstract

Let ${\mathbb{B}}^2$ denote the open unit ball in ${\mathbb{C}}^2$, and let $p\in {\mathbb{C}}^2\setminus \overline{{\mathbb{B}}^2}$. We prove that if $f$ is an analytic function on the sphere $\partial {\mathbb{B}}^2$ 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.

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

References in corpus (2)

• Holomorphic extension from the sphere to the ball
• Extremal discs and the holomorphic extension from convex hypersurfaces