Analyticity for singular sums of squares of degenerate vector fields

Author:
David S. Tartakoff

Journal:
Proc. Amer. Math. Soc. **134** (2006), 3343-3352

MSC (2000):
Primary 35H10; Secondary 35N15

DOI:
https://doi.org/10.1090/S0002-9939-06-08419-X

Published electronically:
May 12, 2006

MathSciNet review:
2231919

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Abstract | References | Similar Articles | Additional Information

Abstract: Recently J. J. Kohn (2005) proved hypoellipticity for

*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

**1.**A. BOVE, M. DERRIDJ, J.J. KOHN AND D.S. TARTAKOFF,*Hypoellipticity for a sum of squares of complex vector fields with large loss of derivatives,*preprint.**2.**A. BOVE AND D.S. TARTAKOFF,*Analytic hypo-ellipticity at non-symplectic characteristics when the symplectic form changes its rank,*preprint.**3.**M CHRIST,*A remark on sums of squares of complex vector fields,*preprint, arXiv:math.CV/0503506.**4.**M. DERRIDJ AND D.S. TARTAKOFF,*Local analyticity for and the -Neumann problem at certain weakly pseudoconvex points,*Commun. in Partial Differential Equations**13(12)**(1988), pp. 1521-1600. MR**0970155 (89m:35158)****5.**M. DERRIDJ AND D.S. TARTAKOFF,*Analyticity and loss of derivatives,*Annals of Mathematics**162(2)**(2005), as Appendix to*Hypoellipticity and loss of derivatives,*by J. J. Kohn in the same issue.**6.**F. HIRZEBRUCH,*Topological Methods in Algebraic Geometry,*Springer-Verlag, New York, 1966. MR**0202713 (34:2573)****7.**J.J. KOHN,*Hypoellipticity and loss of derivatives,*Annals of Mathematics**162(2)**(2005).**8.**C. PARENTI AND A. PARMEGGIANI,*A Note on Kohn's and Christ's Examples,*preprint.**9.**Y.-T. SIU,*Extension of twisted pluricanonical sections with plurisubharmonic weight and invariance of semipositively twisted plurigenera for manifolds not necessarily of general type,*in*Complex Geometry: Collection of Papers Dedicated to Professor Hans Grauert*, 223-277, Springer-Verlag, New York, 2002. MR**1922108 (2003j:32027a)****10.**D.S. TARTAKOFF,*Local analytic hypoellipticity for on non-degenerate Cauchy Riemann manifolds,*Proc. Nat. Acad. Sci. U.S.A.**75**(1978), pp. 3027-3028. MR**0499657 (80g:58045)****11.**D.S. TARTAKOFF,*On the local real analyticity of solutions to and the -Neumann problem,*Acta Math.**145**(1980), pp. 117-204. MR**0590289 (81k:35033)****12.**F. TREVES,*Analytic hypo-ellipticity of a class of pseudo-differential operators with double characteristics and application to the -Neumann problem,*Comm. in P.D.E.**3**(6-7) (1978), pp. 475-642. MR**0492802 (58:11867)**

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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:
https://doi.org/10.1090/S0002-9939-06-08419-X

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.