Advertisement

Mathematische Annalen

, Volume 283, Issue 1, pp 97–119 | Cite as

Asymptotics for some green kernels on the Heisenberg group and the Martin boundary

  • H. Hueber
  • D. Müller
Article

Keywords

Heisenberg Group Martin Boundary Green Kernel 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Brélot, M.: On topological boundaries in potential theory. (Lecture notes in mathematics, Vol. 175.) Berlin Heidelberg New York: Springer 1971Google Scholar
  2. 2.
    Courant, R.: Vorlesungen über Differential- und Integralrechnung 1. Berlin Heidelberg New York: Springer 1971Google Scholar
  3. 3.
    Cygan, J.: Fundamental solution of the heat equation on the Heisenberg group. Preprint, Polish academy of mathematicsGoogle Scholar
  4. 4.
    Erdéily, A., Magnus, W., Oberhettinger, F., Tricomi, F.G.: (Higher transcendental functions, Vol. 2). New York: McGraw-Hill 1953Google Scholar
  5. 5.
    Folland, G.B., Stein, E.M.: Hardy spaces on homogeneous groups. Princeton: Princeton University Press 1982Google Scholar
  6. 6.
    Gaveau, B.: Principe de moindre action, propagation de la chaleur et estimées sous elliptiques sur certains groupes nilpotents. Acta Math.139, 59–153 (1977)Google Scholar
  7. 7.
    Helffer, B., Nourrigat, J.: Caractérisation des opérateurs hypoelliptiques homogènes invariants à gauche sur un groupe de Lie nilpotent gradué. Commun. Partial Differ. Equations4, 899–958 (1979)Google Scholar
  8. 8.
    Helms, L.L.: Introduction to potential theory. (Pure and applied Mathematics, Vol. 22) New York London Sydney Toronto: Wiley 1969Google Scholar
  9. 9.
    Hervé, R.M., Hervé, M.: Les fonctions sur-harmoniques dans l'axiomatique de M. Brélot associeés à un opérateur elliptique dégénéré. Ann. Inst. Fourier22 (2), 131–145 (1972)Google Scholar
  10. 10.
    Hörmander, L.: Hypoelliptic second-order differential equations. Acta Math.119, 147–171 (1967)Google Scholar
  11. 11.
    Hulanicki, A.: The distribution of energy in the Brownian motion in Gaussian field and analytic hypoellipticity of certain subelliptic operators on the Heisenberg group. Stud. Math.56, 165–173 (1976)Google Scholar
  12. 12.
    Margulis, G.A.: Positive harmonic functions on nilpotent groups. Sov. Math.7, 241–243 (1966)Google Scholar
  13. 13.
    Rockland, C.: Hypoellipticity for the Heisenberg group. Trans. Am. Math. Soc.240, 1–52 (1978)Google Scholar

Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • H. Hueber
    • 1
  • D. Müller
    • 1
  1. 1.Fakultät für MathematikUniversität BielefeldBielefeldFederal Republic of Germany

Personalised recommendations