The involutive structure on the blow-up of Rⁿ in Cⁿ

1996/11/07 by Michael Eastwood, Eastwood, Michael, C. Robin Graham +1 · 1 citation
Mathematics · #Advanced Differential Equations and Dynamical Systems #Mathematics and Applications #Meromorphic and Entire Functions #math.CV #msc:32

paper · pdf · doi:10.48550/arxiv.math/9611201

arxiv created 1996/11/07 · arxiv updated 2009/11/30

Abstract

We investigate the natural involutive structure on the blow-up of \Bbb Rⁿ in \Bbb Cⁿ extending the complex structure on the complement of the exceptional hypersurface. Our main result is that this structure is hypocomplex, meaning that any solution is locally a holomorphic function of a basic set of independent solutions. We show this by an elementary power series argument but note that the result is essentially equivalent to the Edge of the Wedge Theorem. In particular, we obtain a relatively simple new proof of this classical theorem.

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• Edge of the Wedge Theory in Hypo-Analytic Manifolds

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