1999/08/02 by Michael G. Eastwood, Eastwood, Michael G., C. Robin Graham +1
Engineering · Mathematics · #32D15 (Primary) 32F25 (Secondary) #Advanced Numerical Analysis Techniques #Algebraic and Geometric Analysis #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #math.CV #msc:32D15 #msc:32F25
paper · pdf · doi:10.48550/arxiv.math/9908009
17 pages, 1 figure. This revised version remarks on how our results compare with an extension theorem of Tumanov
openalex publication_date 1999/08/02 · arxiv created 1999/12/16 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Lewy extension theorem asserts the holomorphic extendability of CR functions defined in a neighborhood of a point on a hypersurface in Cn+1. The edge-of-the-wedge theorem asserts the extendability of holomorphic functions defined in wedges in Cn+1 with edge a maximally real submanifold. In this article we prove under suitable hypotheses the holomorphic extendability to an open set in Cn+1 of CR functions defined in the intersection of a hypersurface with a wedge whose edge is contained in the hypersurface. Unlike the situation for the classical edge-of-the-wedge theorem, for this hypersurface version extendability generally depends on the direction of the wedge.