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CR Runge Sets on Hypersurface Graphs

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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 ℂn, 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 ℂn 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.

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Authors and Affiliations

  1. Department of Mathematics, Texas A&M University, College Station, TX, 77843, USA

    Al Boggess

  2. Department of Mathematics, University of Missouri, Rolla, MO, 65409, USA

    Roman Dwilewicz

  3. Faculty of Mathematics, Cardinal Stefan Wyszyński University, 01-815, Warsaw, Poland

    Roman Dwilewicz

  4. Department of Systems Biology and Translational Medicine, College of Medicine, Texas A&M Health Science Center, Temple, TX, 76504, USA

    Dan Jupiter

Authors
  1. Al Boggess
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  2. Roman Dwilewicz
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  3. Dan Jupiter
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Corresponding author

Correspondence to Roman Dwilewicz.

Additional information

Communicated by Steven Bell.

R. Dwilewicz is partially supported by the Polish Science Foundation (KBN) grant N201 019 32/805.

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Boggess, A., Dwilewicz, R. & Jupiter, D. CR Runge Sets on Hypersurface Graphs. J Geom Anal 18, 980–1001 (2008). https://doi.org/10.1007/s12220-008-9045-8

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  • DOI: https://doi.org/10.1007/s12220-008-9045-8

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