Acta Mathematica

, Volume 187, Issue 2, pp 191–212 | Cite as

Local solvability for a class of differential complexes

  • Paulo D. Cordaro
  • Jorge G. Hounie
Article

Keywords

Local Solvability Differential Complex 

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References

  1. [Br]
    Bredon, G. E.,Sheaf Theory, 2nd edition. Graduate Texts in Math., 170. Springer-Verlag, New York, 1997.Google Scholar
  2. [BT]
    Baouendi, M. S. &Treves, F., A property of the functions and distributions annihilated by a locally integrable system of complex vector fields.Ann. of Math. (2), 113 (1981), 387–421.CrossRefMathSciNetGoogle Scholar
  3. [ChT]
    Chanillo, S. &Treves, F., Local exactness in a class of differential complexes.J. Amer. Math. Soc., 10 (1997), 393–426.CrossRefMathSciNetGoogle Scholar
  4. [CH1]
    Cordaro, P. D. &Hounie, J., On local solvability of underdetermined systems of vector fields.Amer. J. Math., 112 (1990), 243–270.MathSciNetGoogle Scholar
  5. [CH2]
    —, Local solvability for top degree forms in a class of systems of vector fields.Amer. J. Math., 121 (1999), 487–495.MathSciNetGoogle Scholar
  6. [CT1]
    Cordaro, P. D. &Treves, F., Homology and cohomology in hypo-analytic structures of the hypersurface type.J. Geom. Anal., 1 (1991), 39–70.MathSciNetGoogle Scholar
  7. [CT2]
    —,Hyperfunctions on Hypo-Analytic Manifolds. Ann. of Math. Stud., 136. Princeton Univ. Press, Princeton, NJ, 1994.Google Scholar
  8. [CT3]
    —, Necessary and sufficient conditions for the local solvability in hyperfunctions of a class of systems of complex vector fields.Invent. Math., 120 (1995), 339–360.CrossRefMathSciNetGoogle Scholar
  9. [H]
    Hörmander, L.,The Analysis of Linear Partial Differential Operators, IV. Fourier Integral Operators. Grundlehren Math. Wiss., 275, Springer-Verlag, Berlin, 1985.Google Scholar
  10. [MT]
    Mendoza, G. A. &Treves, F., Local solvability in a class of overdetermined systems of linear PDE.Duke Math. J., 63 (1991), 355–377.CrossRefMathSciNetGoogle Scholar
  11. [NT]
    Nirenberg, L. &Treves, F., Solvability of a first order linear partial differential equation.Comm. Pure Appl. Math., 16 (1963), 331–351.MathSciNetGoogle Scholar
  12. [S]
    Stein, E. M.,Singular Integrals and Differentiability Properties of Functions. Princeton Math. Ser., 30. Princeton Univ. Press, Princeton, NJ, 1970.Google Scholar
  13. [T1]
    Treves, F., On the local solvability and local integrability of systems of vector fields.Acta Math., 151 (1983), 1–38.MATHMathSciNetGoogle Scholar
  14. [T2]
    —,Hypo-Analytic Structures. Local Theory. Princeton Math. Ser., 40, Princeton Univ. Press, Princeton, NJ, 1992.Google Scholar

Copyright information

© Institut Mittag-Leffler 2001

Authors and Affiliations

  • Paulo D. Cordaro
    • 1
  • Jorge G. Hounie
    • 2
  1. 1.Department of Mathematics Institute of Mathematics and Statistics (IME)University of São PauloSão PauloBrazil
  2. 2.Department of MathematicsFederal University of São CarlosSão CarlosBrazil

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