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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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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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
  • Received by editor(s): October 4, 2004
  • Published electronically: August 29, 2005
  • Communicated by: Mei-Chi Shaw
  • © Copyright 2005 American Mathematical Society
  • 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
  • MathSciNet review: 2180890