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On the $ C^{\infty }$ wave-front set of traces of CR functions on maximally real submanifolds

Author(s): Z. Adwan; G. Hoepfner
Journal: Proc. Amer. Math. Soc. 136 (2008), 999-1008.
MSC (2000): Primary 35N10; Secondary 42B10, 35A18
Posted: November 26, 2007
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Abstract: We prove that, in a locally integrable structure, the $ C^{\infty }$ wave-front set of the trace of a CR function at a point $ p$ in a totally real submanifold of maximal dimension is independent of the maximally real submanifold passing through the point $ p$.

References:

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M.S. Baouendi, C. H. Chang, and F. Treves, Microlocal hypo-analyticity and extension of CR functions, J. Differential Geom. 18 (1983), 331-391. MR 723811 (85h:32030)

[BH1]
S. Berhanu and J. Hounie, An F. and M. Riesz theorem for planar vector fields, Math. Ann. 320 (2001), 463-485. MR 1846773 (2002f:35057)

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M. G. Eastwood and C. R. Graham, Edge of the wedge theory in hypo-analytic manifolds, Commun. Partial Differ. Equations 28 (2003), 2003-2028. MR 2015410 (2004j:32038)

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F. Treves, Hypo-analytic structures, Local theory, Princeton University Press, 1992. MR 1200459 (94e:35014)

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Additional Information:

Z. Adwan
Affiliation: Department of Mathematics, University of Texas at Brownsville, Brownsville, Texas 78520
Email: adwan@utb.edu

G. Hoepfner
Affiliation: Department of Mathematics, Temple University, Philadelphia, Pennsylvania 19122
Email: hoepfner@temple.edu

DOI: 10.1090/S0002-9939-07-09243-X
PII: S 0002-9939(07)09243-X
Keywords: $C^{\infty }$ wave-front set, locally integrable structure, FBI transform, maximally real submanifold
Received by editor(s): December 15, 2006
Posted: November 26, 2007
Communicated by: David S. Tartakoff
Copyright of article: Copyright 2007, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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