Skip to main content

Analyticity of solutions of partial differential equations on nilpotent lie groups

Part of the Lecture Notes in Mathematics book series (LNM,volume 1077)

Keywords

  • Differential Operator
  • Heisenberg Group
  • Pseudodifferential Operator
  • Heisenberg Algebra
  • Homogeneous Operator

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   44.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   59.00
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. M. S. Baouendi and C. Goulaouic, "Nonanalytic hypoellipticity for some degenerate elliptic operators," Bull. A.M.S. 78 (1972), 483–486.

    CrossRef  MathSciNet  MATH  Google Scholar 

  2. L. Boutet de Monvel and P. Kree, "Pseudodifferential operators and Gevrey classes," Ann. Inst. Fourier, Grenoble 17 1 (1967), 295–323.

    CrossRef  MathSciNet  MATH  Google Scholar 

  3. A. Grigis and L. P. Rothschild, "A criterion for analytic hypoellipticity of of a class of differential operators with polynomial coefficients," Ann. of Math. (to appear).

    Google Scholar 

  4. V. V. Grusin, "On a class of hypoelliptic operators," Mat. Sb. 83 (1970) 456–473 [Math. U.S.S.R. Sb. 12 (1972) 458–476].

    MathSciNet  Google Scholar 

  5. B. Helffer, "Conditions nécessaires d'hypoanalyticité pour des opérateurs invariants à gauche homogènes sur un groupe nilpotent gradué," J. Diff. Eq. 44 (1982), 460–581.

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. _____ and J. Nourrigat, "Caracterisation des operateurs hypoelliptiques homogenes invariants a gauche sur un groupe nilpotent gradue," Comm. P.D.E. 4 (1979), 899–958.

    CrossRef  MathSciNet  MATH  Google Scholar 

  7. L. Hörmander, Linear partial differential equations, Springer-Verlag, Heidelberg-New York (1969).

    MATH  Google Scholar 

  8. _____, "Hypoelliptic second order differential operators", Acta Math. 119 (1967), 147–171.

    CrossRef  MathSciNet  MATH  Google Scholar 

  9. _____, "Uniqueness theorems and wave front sets," Comm. Pure Appl. Math., 24 (1971), 671–704.

    CrossRef  MathSciNet  MATH  Google Scholar 

  10. T. Kato, "Perturbation theory of linear operators," 2nd edition, Springer-Verlag, Berlin-Heidelberg-New York (1980).

    MATH  Google Scholar 

  11. J. J. Kohn, "Boundaries of complex manifolds," Proc. Conf. on Complex Manifolds, Minneapolis (1964), 81–94.

    Google Scholar 

  12. G. Métivier, "Hypoellipticité analytique sur des groupes nilpotents de rang 2," Duke Math. J. 17 (1980).

    Google Scholar 

  13. _____, "Analytic hypoellipticity for operators with multiple characteristics," Comm. P.D.E. 6 (1) (1981), 1–90.

    MathSciNet  MATH  Google Scholar 

  14. _____, "Une classe d'opérateurs non-hypoelliptiques analytiques," Seminaire Goulaouic-Schwartz, Ecole Polytechnique (1979).

    Google Scholar 

  15. C. Rockland, "Hypoellipticity on the Heisenberg group," Trans. A. M. S. 240 (1978) no. 517, 1–52.

    CrossRef  MathSciNet  MATH  Google Scholar 

  16. J. Sjöstrand, "Parametrices for pseudodifferential operators with multiple characteristics," Ark. for Mat. 12 (1974), 85–130.

    CrossRef  MathSciNet  MATH  Google Scholar 

  17. D. Tartakoff, "The analytic hypoellipticity of \(\bar \partial _b\) and related operators on nondegenerate C-R manifolds," Acta Math. 145 (3–4) (1980), 177–203.

    CrossRef  MathSciNet  Google Scholar 

  18. F. Trèves, "Analytic hypoellipticity of a class of pseudodifferential operators," Comm. P.D.E. 3 (1978), 475–642.

    CrossRef  MATH  Google Scholar 

  19. _____, Introduction to pseudodifferential operators and Fourier integral operators, Vol. 1, The University Series in Mathematics, Plenum Press, New York, (1980).

    CrossRef  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1984 Springer-Verlag

About this paper

Cite this paper

Rothschild, L.P. (1984). Analyticity of solutions of partial differential equations on nilpotent lie groups. In: Herb, R., Johnson, R., Lipsman, R., Rosenberg, J. (eds) Lie Group Representations III. Lecture Notes in Mathematics, vol 1077. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0072346

Download citation

  • DOI: https://doi.org/10.1007/BFb0072346

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-13385-8

  • Online ISBN: 978-3-540-38936-1

  • eBook Packages: Springer Book Archive