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Global approximation of CR functions on Bloom-Graham model graphs in $\mathbb{C} ^n$


Authors: Albert Boggess and Daniel Jupiter
Journal: Proc. Amer. Math. Soc. 134 (2006), 723-730
MSC (2000): Primary 32V10, 32V99, 30E10
DOI: https://doi.org/10.1090/S0002-9939-05-08227-4
Published electronically: August 29, 2005
MathSciNet review: 2180890
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Abstract: We define a class of generic CR submanifolds of $\mathbb{C} ^n$ of real codimension $d$, $1\leq d\leq n$, 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.


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Additional Information

Albert Boggess
Affiliation: Department of Mathematics, Texas A & M University, College Station, Texas 77843-3368
Email: boggess@math.tamu.edu

Daniel Jupiter
Affiliation: Department of Mathematics, Texas A & M University, College Station, Texas 77843-3368
Email: jupiter@math.tamu.edu

DOI: https://doi.org/10.1090/S0002-9939-05-08227-4
Keywords: CR approximation, Bloom-Graham model graphs
Received by editor(s): October 4, 2004
Published electronically: August 29, 2005
Communicated by: Mei-Chi Shaw
Article copyright: © Copyright 2005 American Mathematical Society

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