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

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References

  1. Brélot, M.: On topological boundaries in potential theory. (Lecture notes in mathematics, Vol. 175.) Berlin Heidelberg New York: Springer 1971

    Google Scholar 

  2. Courant, R.: Vorlesungen über Differential- und Integralrechnung 1. Berlin Heidelberg New York: Springer 1971

    Google Scholar 

  3. Cygan, J.: Fundamental solution of the heat equation on the Heisenberg group. Preprint, Polish academy of mathematics

  4. Erdéily, A., Magnus, W., Oberhettinger, F., Tricomi, F.G.: (Higher transcendental functions, Vol. 2). New York: McGraw-Hill 1953

    Google Scholar 

  5. Folland, G.B., Stein, E.M.: Hardy spaces on homogeneous groups. Princeton: Princeton University Press 1982

    Google Scholar 

  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. 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. Helms, L.L.: Introduction to potential theory. (Pure and applied Mathematics, Vol. 22) New York London Sydney Toronto: Wiley 1969

    Google Scholar 

  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. Hörmander, L.: Hypoelliptic second-order differential equations. Acta Math.119, 147–171 (1967)

    Google Scholar 

  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. Margulis, G.A.: Positive harmonic functions on nilpotent groups. Sov. Math.7, 241–243 (1966)

    Google Scholar 

  13. Rockland, C.: Hypoellipticity for the Heisenberg group. Trans. Am. Math. Soc.240, 1–52 (1978)

    Google Scholar 

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Hueber, H., Müller, D. Asymptotics for some green kernels on the Heisenberg group and the Martin boundary. Math. Ann. 283, 97–119 (1989). https://doi.org/10.1007/BF01457504

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