2006/06/16 by Luca Baracco, L. Baracco, Baracco, L. +3
Computer Science · Mathematics · #32 #Advanced Algebra and Logic #Complex Variables (math.CV) #FOS: Mathematics #math.CV #msc:32
paper · pdf · doi:10.48550/arxiv.math/0606390
13 pages
arxiv created 2006/06/16 · openalex publication_date 2006/06/16 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In \C2=\R2+i\R2 with coordinates z=(z1,z2), z=x+iy, we consider a function f continuous on a domain Ω of \R2 separately real analytic in x1 and CR extendible to y2 (resp. CR extendible to y2>0). This means that f(⋅,x2) extends holomorphically for |y1|<εx2 and f(x1,⋅) for | y2|<ε (resp. 0≤ y2<ε continuous up to y2=0) with ε independent of x1. We prove in Theorem 3.4 that f is then real analytic (resp. in Theorem 3.5 that it extends holomorphically to a "wedge" W= Ω+iΓε where Γε is an open cone trumcated by |y|<ε and containing the ray 0<y2<ε).