### Abstract

We define a class of generic CR submanifolds of ℂ ^{n} of real codimension d, 1 ≤ d ≤ n, called the Bloom-Graham model graphs, whose graphing functions are partially decoupled in their dependence on the variables in the real directions. We prove a global version of the Baouendi-Treves CR approximation theorem for Bloom-Graham model graphs with a polynomial growth assumption on their graphing functions.

Original language | English (US) |
---|---|

Pages (from-to) | 723-730 |

Number of pages | 8 |

Journal | Proceedings of the American Mathematical Society |

Volume | 134 |

Issue number | 3 |

DOIs | |

State | Published - Mar 2006 |

Externally published | Yes |

### Fingerprint

### Keywords

- Bloom-Graham model graphs
- CR approximation

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

**Global approximation of CR functions on bloom-graham model graphs in ℂ ^{n} .** / Boggess, Albert; Jupiter, Daniel.

Research output: Contribution to journal › Article

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*Proceedings of the American Mathematical Society*, vol. 134, no. 3, pp. 723-730. https://doi.org/10.1090/S0002-9939-05-08227-4

}

TY - JOUR

T1 - Global approximation of CR functions on bloom-graham model graphs in ℂ n

AU - Boggess, Albert

AU - Jupiter, Daniel

PY - 2006/3

Y1 - 2006/3

N2 - We define a class of generic CR submanifolds of ℂ n of real codimension d, 1 ≤ d ≤ n, called the Bloom-Graham model graphs, whose graphing functions are partially decoupled in their dependence on the variables in the real directions. We prove a global version of the Baouendi-Treves CR approximation theorem for Bloom-Graham model graphs with a polynomial growth assumption on their graphing functions.

AB - We define a class of generic CR submanifolds of ℂ n of real codimension d, 1 ≤ d ≤ n, called the Bloom-Graham model graphs, whose graphing functions are partially decoupled in their dependence on the variables in the real directions. We prove a global version of the Baouendi-Treves CR approximation theorem for Bloom-Graham model graphs with a polynomial growth assumption on their graphing functions.

KW - Bloom-Graham model graphs

KW - CR approximation

UR - http://www.scopus.com/inward/record.url?scp=33644780610&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33644780610&partnerID=8YFLogxK

U2 - 10.1090/S0002-9939-05-08227-4

DO - 10.1090/S0002-9939-05-08227-4

M3 - Article

AN - SCOPUS:33644780610

VL - 134

SP - 723

EP - 730

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 3

ER -