Title

CR Runge Sets on Hypersurface Graphs

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.

Department(s)

Mathematics and Statistics

Sponsor(s)

Polish Science Foundation

Keywords and Phrases

CR functions; CR runge sets; Holomorphic approximation

Library of Congress Subject Headings

CR submanifolds

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2008 Springer Verlag, All rights reserved.


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