Separate holomorphic extension along lines and holomorphic extension from the sphere to the ball

Abstract

We give positive answer to a conjecture by Agranovsky. A continuous function on the sphere which has separate holomorphic extension along the set of complex lines passing through three non aligned interior points, is the trace of a holomorphic function in the ball.

6 pages

References in corpus (1)

• Small families of complex lines for testing holomorphic extendibility