CR Runge Sets on Hypersurface Graphs |
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| Authors: | Al Boggess Roman Dwilewicz Dan Jupiter |
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| Institution: | (1) Department of Mathematics, Texas A&M University, College Station, TX 77843, USA;(2) Department of Mathematics, University of Missouri, Rolla, MO 65409, USA;(3) Faculty of Mathematics, Cardinal Stefan Wyszyński University, 01-815 Warsaw, Poland;(4) Department of Systems Biology and Translational Medicine, College of Medicine, Texas A&M Health Science Center, Temple, TX 76504, USA |
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| Abstract: | 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.
R. Dwilewicz is partially supported by the Polish Science Foundation (KBN) grant N201 019 32/805. |
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| Keywords: | CR functions CR Runge sets Holomorphic approximation |
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