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A Radó Theorem for Locally Solvable Structures of Co-rank One

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Complex Analysis

Part of the book series: Trends in Mathematics ((TM))

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Abstract

We extend the classical theorem of Radó to locally solvable structures of co-rank one. One of the main tools in the proof is a refinement of the Baouendi-Treves approximation theorem that may be of independent interest.

Work supported in part by CNPq, FINEP and FAPESP.

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References

  1. H. Alexander, Removable sets for CR functions, Several complex variables (Stockholm, 1987/1988), Math. Notes, 38, Princeton Univ. Press, Princeton, NJ, (1993), 1–7.

    Google Scholar 

  2. M.S. Baouendi and F. Treves, A property of the functions and distributions annihilated by a locally integrable system of complex vector fields, Ann. of Math. 113 (1981), 387–421.

    Article  MathSciNet  Google Scholar 

  3. M.S. Baouendi and F. Treves, A local constancy principle for the solutions of certain overdetermined systems of first-order linear partial differential equations, Math. Analysis and Applications, Part A, Advances in Math. Supplementary Studies 7A (1981), 245–262.

    MathSciNet  Google Scholar 

  4. S. Berhanu, P. Cordaro and J. Hounie, An Introduction to Involutive Structures, Cambridge University Press, 2007. 432 p.

    Google Scholar 

  5. E.M. Chirka, Radó’s theorem for CR-mappings of hypersurfaces, (Russian. Russian summary) Mat. Sb. 185 (1994), 6, 125–144; translation in Russian Acad. Sci. Sb. Math. 82 (1995), 243–259.

    Google Scholar 

  6. E.M. Chirka, A generalization of Radó’s theorem, Ann. Polonici Math. 84, (2003), 109–112.

    Article  MathSciNet  Google Scholar 

  7. P.D. Cordaro and J. Hounie, Local solvability for a class of differential complexes, Acta Math. 187 (2001), 191–212.

    Article  MATH  MathSciNet  Google Scholar 

  8. P.D. Cordaro and F. Treves, Homology and cohomology in hypo-analytic structures of the hypersurface type, J. Geometric Analysis, 1 (1991), 39–70.

    MATH  MathSciNet  Google Scholar 

  9. J. Hounie and J. Tavares, Radó’s theorem for locally solvable vector fields, Proc. Amer. Math. Soc. 119 (1993), 829–836.

    MATH  MathSciNet  Google Scholar 

  10. G. Mendoza and F. Treves Local solvability in a class of overdetermined systems of linear PDE, Duke Math. J. 63 (1991), 355–377.

    Article  MATH  MathSciNet  Google Scholar 

  11. J.-P. Rosay, and E. Stout, Radó’s theorem for C-R functions, Proc. Amer. Math. Soc. 106 (1989), 1017–1026.

    MATH  MathSciNet  Google Scholar 

  12. E.L. Stout, A generalization of a theorem of Radó, Math. Ann. 177 (1968), 339–340.

    Article  MATH  MathSciNet  Google Scholar 

  13. H.J. Sussmann, Orbits of families of vector fields and integrability of distributions, Trans. Amer. Math. Soc. 180 (1973), 171–188.

    Article  MATH  MathSciNet  Google Scholar 

  14. F. Treves, Approximation and representation of functions and distributions annihilated by a system of complex vector fields, École Polytech., Centre de Math., Palaiseau, France, (1981).

    MATH  Google Scholar 

  15. F. Treves, Hypo-analytic structures, Princeton University Press, (1992).

    Google Scholar 

  16. F. Treves, On the local solvability and local integrability of systems of vector fields, Acta Math. 151, 1983, 1–38.

    Article  MATH  MathSciNet  Google Scholar 

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Dedicated to Linda Rothschild

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Hounie, J. (2010). A Radó Theorem for Locally Solvable Structures of Co-rank One. In: Complex Analysis. Trends in Mathematics. Birkhäuser Basel. https://doi.org/10.1007/978-3-0346-0009-5_11

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