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| Title: | CR runge sets on hypersurface graphs |
| Author (s): | Boggess, Al Dwilewicz, Roman Jupiter, Dan |
| Department/Lab Affiliations: | Mathematics & Statistics |
| Keywords: | CR functions CR runge sets Holomorphic approximation |
| Subject Terms: | CR submanifolds. |
| Issue Date: | 2008-10 |
| Publisher: | Springer Verlag |
| Citation: | Boggess, Al, Roman Dwilewicz, and Dan Jupiter. CR Runge sets on hypersurface graphs, Journal of Geometric Analysis, 2008. |
| 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. |
| Type: | Article - Journal text |
| In Title: | Journal of Geometric Analysis |
| Copyright Notice: | This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder. Pre-print: author can archive; Post-print: author can archive; FULL COPYRIGHT INFORMATION: |
| Publisher URL: | |
| Link to this page: |
| title | CR runge sets on hypersurface graphs |
| contributor.author | Boggess, Al |
| contributor.author | Dwilewicz, Roman |
| contributor.author | Jupiter, Dan |
| contributor.deptlab | Mathematics & Statistics |
| contributor.sponsor | Polish Science Foundation |
| subject | CR functions |
| subject | CR runge sets |
| subject | Holomorphic approximation |
| subject.LCSH | CR submanifolds. |
| date.issued | 2008-10 |
| publisher | Springer Verlag |
| identifier.citation | Boggess, Al, Roman Dwilewicz, and Dan Jupiter. CR Runge sets on hypersurface graphs, Journal of Geometric Analysis, 2008. |
| identifier.pub.URI | |
| description.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. |
| type | Article - Journal |
| type.DCMIType | text |
| type.status | Postprint |
| rights | This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder. |
| rights | Pre-print: author can archive; Post-print: author can archive; |
| rights.URI | |
| rights.URI | |
| relation.isPartOf | Journal of Geometric Analysis |
| date.available | 2008-09-12T20:43:45Z |
| identifier.persist.URI |