CR Runge Sets on Hypersurface Graphs
This work contains an improvement of earlier results of Boggess and Dwilewicz regarding global approximation of CR functions by entire functions in the case of hypersurface graphs. In this work, we show that if ω, an open subset of a real hypersurface in ℂ n , can be graphed over a convex subset in ℝ2n−1, then ω is CR-Runge in the sense that continuous CR functions on ω can be approximated by entire functions on ℂ n in the compact open topology of ω. Examples are presented to show that this approximation result does not hold for graphed CR submanifolds in higher codimension.
A. Boggess et al., "CR Runge Sets on Hypersurface Graphs," Journal of Geometric Analysis, Springer Verlag, Oct 2008.
Mathematics and Statistics
Polish Science Foundation
Keywords and Phrases
CR Functions; CR Runge Sets; Holomorphic Approximation; CR Submanifolds
Article - Journal
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