CR runge sets on hypersurface graphs

Al Boggess, Roman Dwilewicz, Daniel Jupiter

Research output: Contribution to journalArticle

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 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.

Original languageEnglish (US)
Pages (from-to)980-1001
Number of pages22
JournalJournal of Geometric Analysis
Volume18
Issue number4
DOIs
StatePublished - Oct 2008
Externally publishedYes

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CR Functions
Entire Function
Hypersurface
CR-submanifold
Compact-open Topology
Real Hypersurfaces
Subset
Approximation
Graph in graph theory
Codimension
Continuous Function

Keywords

  • CR functions
  • CR Runge sets
  • Holomorphic approximation

ASJC Scopus subject areas

  • Geometry and Topology

Cite this

CR runge sets on hypersurface graphs. / Boggess, Al; Dwilewicz, Roman; Jupiter, Daniel.

In: Journal of Geometric Analysis, Vol. 18, No. 4, 10.2008, p. 980-1001.

Research output: Contribution to journalArticle

Boggess, Al ; Dwilewicz, Roman ; Jupiter, Daniel. / CR runge sets on hypersurface graphs. In: Journal of Geometric Analysis. 2008 ; Vol. 18, No. 4. pp. 980-1001.
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