Available in electronic format
Available in print format		 Transacrions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(e) ISSN 0002-9947(p)
Previous issue | Table of contents | Next issue
Articles in press | Recently posted articles | Most recent issue | All issues
Previous Article | Next Article
     

Remarks about global analytic hypoellipticity

Author(s): Adalberto P. Bergamasco
Journal: Trans. Amer. Math. Soc. 351 (1999), 4113-4126.
MSC (1991): Primary 35H05
Posted: March 19, 1999
Retrieve article in: PDF DVI PostScript
This article is available free of charge

Abstract | References | Similar articles | Additional information

Abstract: We present a characterization of the operators

\begin{displaymath}L=\partial/\partial t+(a(t)+ib(t))\partial/\partial x\end{displaymath}

which are globally analytic hypoelliptic on the torus. We give information about the global analytic hypoellipticity of certain overdetermined systems and of sums of squares.

References:

[BT]
M.S. Baouendi and F. Treves, A local constancy principle for the solutions of certain overdetermined systems of first-order linear partial differential equations, Advances in Math. Suppl. Studies 7A (1981), 245-262. MR 84f:35105

[B]
A. Bergamasco, Perturbations of globally hypoelliptic operators, J. Diff. Equations 114 (1994), 513-526. MR 95j:35046

[BCM]
A. Bergamasco, P. Cordaro, and P. Malagutti, Globally hypoelliptic systems of vector fields, J. Funct. Anal. 114 (1993), 267-285. MR 94e:35048

[deB]
N.G. de Bruijn, Asymptotic Methods in Analysis, Dover, New York, 1981. MR 83m:41028

[Ca-Ho]
F. Cardoso and J. Hounie, Globally hypoanalytic first-order evolution equations, An. Acad. Brasil. Ciênc. 49 (1977), 533-535. MR 57:17729

[Co-Hi]
P. Cordaro and A. Himonas, Global analytic hypoellipticity for a class of degenerate elliptic operators on the torus, Mathematical Research Letters 1 (1994), 501-510. MR 95j:35048

[GPY]
T. Gramchev, P. Popivanov, and M. Yoshino, Global properties in spaces of generalized functions on the torus for second order differential operators with variable coefficients, Rend. Sem. Mat. Univ. Pol. Torino 51 (1993), 145-172. MR 95k:35047

[G]
S.J. Greenfield, Hypoelliptic vector fields and continued fractions, Proc. Amer. Math. Soc. 31 (1972), 115-118. MR 46:617

[T1]
F. Treves, Analytic hypoelliptic partial differential equations of principal type, Comm. Pure Appl. Math. 24 (1971), 537-570. MR 45:5569

[T2]
F. Treves, Hypoanalytic Structures, Princeton University Press, Princeton, NJ, 1992. MR 94e:35014

Similar Articles:

Retrieve articles in Transactions of the American Mathematical Society with MSC (1991): 35H05

Retrieve articles in all Journals with MSC (1991): 35H05

Additional Information:

Adalberto P. Bergamasco
Affiliation: Departamento de Matemática, UFSCar, Caixa Postal 676, 13565-905, São Carlos, SP, Brazil
Email: apbergam@power.ufscar.br

DOI: 10.1090/S0002-9947-99-02299-0
PII: S 0002-9947(99)02299-0
Keywords: Global analytic hypoellipticity, exponential Liouville numbers, exponential Liouville vectors, steepest descent, involutive systems, continued fractions.
Received by editor(s): July 19, 1996
Received by editor(s) in revised form: September 29, 1997
Posted: March 19, 1999
Additional Notes: The author was partially supported by CNPq.
Dedicated: Dedicated to Antonio Gilioli, in memoriam
Copyright of article: Copyright 1999, American Mathematical Society

  AMS Website Logo Small Comments: webmaster@ams.org
© Copyright 2008, American Mathematical Society
Privacy Statement 		Search the AMSPowered by Google