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

2010/03/24 by Luca Baracco, L. Baracco, Baracco, L.
Mathematics · #Algebraic and Geometric Analysis #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #Meromorphic and Entire Functions #math.CV

paper · pdf · doi:10.48550/arxiv.1003.4705

6 pages

openalex publication_date 2010/03/24 · arxiv created 2010/12/31 · arxiv updated 2011/01/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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