TY - JOUR
T1 - CR runge sets on hypersurface graphs
AU - Boggess, Al
AU - Dwilewicz, Roman
AU - Jupiter, Dan
N1 - Funding Information:
R. Dwilewicz is partially supported by the Polish Science Foundation (KBN) grant N201 019 32/805.
PY - 2008/10
Y1 - 2008/10
N2 - 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 ℝ 2n-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.
AB - 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 ℝ 2n-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.
KW - CR Runge sets
KW - CR functions
KW - Holomorphic approximation
UR - https://www.scopus.com/pages/publications/84867984701
UR - https://www.scopus.com/pages/publications/84867984701#tab=citedBy
U2 - 10.1007/s12220-008-9045-8
DO - 10.1007/s12220-008-9045-8
M3 - Article
AN - SCOPUS:84867984701
SN - 1050-6926
VL - 18
SP - 980
EP - 1001
JO - Journal of Geometric Analysis
JF - Journal of Geometric Analysis
IS - 4
ER -