Global approximation of CR functions on Bloom-Graham model graphs in ℂⁿ

Boggess, Albert; Jupiter, Daniel

doi:10.1090/S0002-9939-05-08227-4

Global approximation of CR functions on Bloom-Graham model graphs in $\mathbb {C}^n$
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by Albert Boggess and Daniel Jupiter PDF

Proc. Amer. Math. Soc. 134 (2006), 723-730 Request permission

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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