Comportement asymptotique des fonctions harmoniques sur les arbres
Mouton, Frédéric
Séminaire de probabilités de Strasbourg, Tome 34 (2000), p. 353-373 / Harvested from Numdam
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     author = {Mouton, Fr\'ed\'eric},
     title = {Comportement asymptotique des fonctions harmoniques sur les arbres},
     journal = {S\'eminaire de probabilit\'es de Strasbourg},
     volume = {34},
     year = {2000},
     pages = {353-373},
     mrnumber = {1768074},
     zbl = {0958.60049},
     language = {fr},
     url = {http://dml.mathdoc.fr/item/SPS_2000__34__353_0}
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Mouton, Frédéric. Comportement asymptotique des fonctions harmoniques sur les arbres. Séminaire de probabilités de Strasbourg, Tome 34 (2000) pp. 353-373. http://gdmltest.u-ga.fr/item/SPS_2000__34__353_0/

[1] Alano Ancona. Negatively curved manifolds, elliptic operators and the Martin boundary. Ann. of Math., 125:495-536, 1987. | MR 890161 | Zbl 0652.31008

[2] Alano Ancona. Positive harmonic functions and hyperbolicity. In J. Kràl et al., editor, Potential Theory, Surveys and Problems. Springer Lect. Notes in Math. 1344, Berlin, 1988. | MR 973878 | Zbl 0677.31006

[3] M.T. Anderson and R. Schoen. Positive harmonic functions on complete manifolds of negative curvature. Ann. of Math., 121:429-461, 1985. | MR 794369 | Zbl 0587.53045

[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. | Numdam | MR 520013 | Zbl 0377.31009

[5] A.P. Calderón. On a theorem of Marcinkiewicz and Zygmund. Trans. of A.M.S., 68:55-61, 1950. | MR 32864 | Zbl 0035.18903

[6] A.P. Calderón. On the behaviour of harmonic functions at the boundary. Trans. of A.M.S., 68:47-54, 1950. | MR 32863 | Zbl 0035.18901

[7] P. Cartier. Fonctions harmoniques sur un arbre. In Symposia Mathematica, volume IX, pages 203-270. Academic Press, London and New-York, 1972. | MR 353467 | Zbl 0283.31005

[8] Yves Derriennic. Marche aléatoire sur le groupe libre et frontière de Martin. Z. Wahrscheinlichkeitstheorie verw. Gebiete, 32:261-276, 1975. | MR 388545 | Zbl 0364.60117

[9] Richard Durrett. Brownian Motion and Martingales in Analysis. Wadsworth Advanced Books & Software, 1984. | Zbl 0554.60075

[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. | Zbl 0214.44101

[11] Pierre Fatou. Séries trigonométriques et séries de Taylor. Acta Math., 30:335-400, 1906. | JFM 37.0283.01

[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. | MR 492068 | Zbl 0318.31006

[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. | MR 615287 | Zbl 0466.31012

[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. | MR 951187 | Zbl 0637.31004

[15] J. Marcinkiewicz and A. Zygmund. A theorem of Lusin. Duke Math. J., 4:473-485, 1938. | JFM 64.0268.01 | Zbl 0019.42001

[16] Frédéric Mouton. Comportement asymptotique des fonctions harmoniques en courbure négative. Comment. Math. Helvetici, 70:475-505, 1995. | MR 1340105 | Zbl 0840.60018

[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. | MR 1802423 | Zbl 0637.31005

[18] I.I. Privalov. Sur les fonctions conjuguées. Bull. Soc. Math. France, pages 100-103,1916. | Numdam

[19] D.C. Spencer. A function theoric identity. Amer. J. Math., 65:147-160, 1943. | MR 7437 | Zbl 0060.20603

[20] E.M. Stein. On the theory of harmonic functions of several variables II. Acta Math., 106:137-174,1961. | MR 173019 | Zbl 0111.08001