Analyticity for singular sums of squares of degenerate vector fields
Author:
David S. Tartakoff
Journal:
Proc. Amer. Math. Soc. 134 (2006), 33433352
MSC (2000):
Primary 35H10; Secondary 35N15
Published electronically:
May 12, 2006
MathSciNet review:
2231919
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Abstract: Recently J. J. Kohn (2005) proved hypoellipticity for (the negative of) a singular sum of squares of complex vector fields on the complex Heisenberg group, an operator which exhibits a loss of derivatives. Subsequently, M. Derridj and D. S. Tartakoff proved analytic hypoellipticity for this operator using rather different methods going back to earlier methods of Tartakoff. Those methods also provide an alternate proof of the hypoellipticity given by Kohn. In this paper, we consider the equation for which the underlying manifold is only of finite type, and prove analytic hypoellipticity using methods of Derridj and Tartakoff. This operator is also subelliptic with large loss of derivatives, but the exact loss plays no role for analytic hypoellipticity. Nonetheless, these methods give a proof of hypoellipticity with precise loss as well, which is to appear in a forthcoming paper by A. Bove, M. Derridj, J. J. Kohn and the author.
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Additional Information
David S. Tartakoff
Affiliation:
Department of Mathematics, University of Illinois at Chicago, m/c 249, 851 S. Morgan Street, Chicago, Illinois 60607
Email:
dst@uic.edu
DOI:
http://dx.doi.org/10.1090/S000299390608419X
PII:
S 00029939(06)08419X
Received by editor(s):
June 1, 2005
Published electronically:
May 12, 2006
Communicated by:
Eric Bedford
Article copyright:
© Copyright 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
