Comportement asymptotique des fonctions harmoniques sur les arbres

Frédéric Mouton

Séminaire de probabilités de Strasbourg (2000)

  • Volume: 34, page 353-373

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Mouton, Frédéric. "Comportement asymptotique des fonctions harmoniques sur les arbres." Séminaire de probabilités de Strasbourg 34 (2000): 353-373. <http://eudml.org/doc/114047>.

@article{Mouton2000,
author = {Mouton, Frédéric},
journal = {Séminaire de probabilités de Strasbourg},
keywords = {random walk; infinite tree; radial convergence; radial boundedness; finiteness of radial energy; Riemannian manifolds of pinched negative curvature},
language = {fre},
pages = {353-373},
publisher = {Springer - Lecture Notes in Mathematics},
title = {Comportement asymptotique des fonctions harmoniques sur les arbres},
url = {http://eudml.org/doc/114047},
volume = {34},
year = {2000},
}

TY - JOUR
AU - Mouton, Frédéric
TI - Comportement asymptotique des fonctions harmoniques sur les arbres
JO - Séminaire de probabilités de Strasbourg
PY - 2000
PB - Springer - Lecture Notes in Mathematics
VL - 34
SP - 353
EP - 373
LA - fre
KW - random walk; infinite tree; radial convergence; radial boundedness; finiteness of radial energy; Riemannian manifolds of pinched negative curvature
UR - http://eudml.org/doc/114047
ER -

References

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  1. [1] Alano Ancona. Negatively curved manifolds, elliptic operators and the Martin boundary. Ann. of Math., 125:495-536, 1987. Zbl0652.31008MR890161
  2. [2] Alano Ancona. Positive harmonic functions and hyperbolicity. In J. Kràl et al., editor, Potential Theory, Surveys and Problems. SpringerLect. Notes in Math.1344, Berlin, 1988. Zbl0677.31006MR973878
  3. [3] M.T. Anderson and R. Schoen. Positive harmonic functions on complete manifolds of negative curvature. Ann. of Math., 121:429-461, 1985. Zbl0587.53045MR794369
  4. [4] Jean Brossard. Comportement non-tangentiel et comportement brownien des fonctions harmoniques dans un demi-espace. Démonstration probabiliste d'un théorème de Calderon et Stein. Séminaire de Probabilités, Université de Strasbourg, XII:378-397, 1978. Zbl0377.31009MR520013
  5. [5] A.P. Calderón. On a theorem of Marcinkiewicz and Zygmund. Trans. of A.M.S., 68:55-61, 1950. Zbl0035.18903MR32864
  6. [6] A.P. Calderón. On the behaviour of harmonic functions at the boundary. Trans. of A.M.S., 68:47-54, 1950. Zbl0035.18901MR32863
  7. [7] P. Cartier. Fonctions harmoniques sur un arbre. In Symposia Mathematica, volume IX, pages 203-270. Academic Press, London and New-York, 1972. Zbl0283.31005MR353467
  8. [8] Yves Derriennic. Marche aléatoire sur le groupe libre et frontière de Martin. Z. Wahrscheinlichkeitstheorie verw. Gebiete, 32:261-276, 1975. Zbl0364.60117MR388545
  9. [9] Richard Durrett. Brownian Motion and Martingales in Analysis. Wadsworth Advanced Books & Software, 1984. Zbl0554.60075
  10. [10] E.B. Dynkin and M.B. Malyutov. Random walks on groups with a finite number of generators. Soviet Math. Dokl., 2:399-402, 1961. Zbl0214.44101
  11. [11] Pierre Fatou. Séries trigonométriques et séries de Taylor. Acta Math., 30:335-400, 1906. Zbl37.0283.01JFM37.0283.01
  12. [12] A. Korânyi and R.B. Putz. Local Fatou theorem and area theorem for symmetric spaces of rank one. Trans. Amer. Math. Soc., 224:157-168,1976. Zbl0318.31006MR492068
  13. [13] A. Korányi and R.B. Putz. An area theorem for products of symmetric spaces of rank one. Bull. Sc. math., 105:3-16, 1981. Zbl0466.31012MR615287
  14. [14] Adam Korânyi, Massimo A. Picardello, and Mitchell H. Taibleson. Hardy spaces on non-homogeneous trees. In Symposia Mathematica, volume XXIX, pages 205-254. Academic Press, London and New-York, 1987. Zbl0637.31004MR951187
  15. [15] J. Marcinkiewicz and A. Zygmund. A theorem of Lusin. Duke Math. J., 4:473-485, 1938. Zbl0019.42001JFM64.0268.01
  16. [16] Frédéric Mouton. Comportement asymptotique des fonctions harmoniques en courbure négative. Comment. Math. Helvetici, 70:475-505, 1995. Zbl0840.60018MR1340105
  17. [17] Massimo A. Picardello and Wolfgang Woess. Finite truncations of random walks on trees. In Symposia Mathematica, volume XXIX, pages 255-265. Academic Press, London and New-York, 1987. Zbl0637.31005MR1802423
  18. [18] I.I. Privalov. Sur les fonctions conjuguées. Bull. Soc. Math. France, pages 100-103,1916. Zbl46.0540.03
  19. [19] D.C. Spencer. A function theoric identity. Amer. J. Math., 65:147-160, 1943. Zbl0060.20603MR7437
  20. [20] E.M. Stein. On the theory of harmonic functions of several variables II. Acta Math., 106:137-174,1961. Zbl0111.08001MR173019

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