Holomorphic extension from the sphere to the ball

Abstract

Real analytic functions on the boundary of the sphere which have separate holomorphic extension along the complex lines through a boundary point have holomorphic extension to the ball. This was proved in a previous preprint by an argument of CR geometry. We give here an elementary proof based on the expansion in holomorphic and antiholomorphic powers.

References in corpus (2)

• Holomorphic extension from a convex hypersurface
• Holomorphic extension from the unit sphere in ${\mathbb{C}}^n$ into complex lines passing through a finite set

Cited by in corpus (3)

• Small families of complex lines for testing holomorphic extendibility
• Meromorphic extensions from small families of circles and holomorphic extensions from spheres
• Orthogonal testing families and holomorphic extension from the sphere to the ball