Holomorphic extension from the sphere to the ball

Details Holomorphic extension from the sphere to the ball Holomorphic extension from the sphere to the ball

2009-11-13

arxiv.org/abs/0911.2560v1

Mathematics

Complex Variables

Scientific paper

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.

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