Liouville theorems based on symmetric diffusions
Bulletin de la Société Mathématique de France, Tome 124 (1996) no. 4, pp. 545-557.
@article{BSMF_1996__124_4_545_0,
     author = {Kaneko, Hiroshi},
     title = {Liouville theorems based on symmetric diffusions},
     journal = {Bulletin de la Soci\'et\'e Math\'ematique de France},
     pages = {545--557},
     publisher = {Soci\'et\'e math\'ematique de France},
     volume = {124},
     number = {4},
     year = {1996},
     doi = {10.24033/bsmf.2292},
     mrnumber = {98a:31005},
     zbl = {0870.31013},
     language = {en},
     url = {http://www.numdam.org/articles/10.24033/bsmf.2292/}
}
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Kaneko, Hiroshi. Liouville theorems based on symmetric diffusions. Bulletin de la Société Mathématique de France, Tome 124 (1996) no. 4, pp. 545-557. doi : 10.24033/bsmf.2292. http://www.numdam.org/articles/10.24033/bsmf.2292/

[B-H] Bouleau (N.) and Hirsch (F.). - Dirichlet forms and Analysis on Wiener space. - Walter de Gruyter, Berlin, 1991. | MR | Zbl

[B-M1] Biroli (M.) et Mosco (U.). - Formes de Dirichlet et estimations structurelles dans les milieux discontinus, C. R. Acad. Sci. Paris, t. 313, 1991, p. 593-598. | MR | Zbl

[B-M2] Biroli (M.) and Mosco (U.). - A Saint-Venant principle for Dirichlet forms on discontinuous media, Elenco Preprint, Rome, 1991.

[C-Y] Cheng (S.Y.) and Yau (S.T.). - Differential Equations on Riemannian manifolds and their geometric applications, Comm. Pure Appl. Math., t. 28, 1975, p. 333-354. | MR | Zbl

[F1] Fukushima (M.). - On holomorphic diffusions and plurisubharmonic functions, Contemporary Math, t. 78, 1988. | MR | Zbl

[F2] Fukushima (M.). - On recurrence criteria in the Dirichlet space theory, in From local times to global geometry, control and physics, Longman Scientific &x0026; Technical. - K.D. Elworthy, Essex, 1984-1985.

[F-0] Fukushima (M.) and Okada (M.). - On Dirichlet forms for plurisubharmonic functions, Acta Math., t. 159, 1988, p. 171-214. | MR | Zbl

[F-O-T] Fukushima (M.), Oshima (M.) and Takeda (M.). - Dirichlet forms and symmetric Markov processes. - Walter de Gruyter, Berlin, 1994. | Zbl

[H] Hahn (H.). - Über die Integrale des Herrn Hellinger und die Orthogonalinvarianten der quadratischen Formen von unendlich vielen Veränderlichen, Monatsh. für Math. und Physik, t. 23, 1912, p. 161-224. | JFM

[K] Kaneko (H.). - A stochastic approach to a Liouville property for plurisubharmonic functions, J. Math. Soc. Japan, t. 41, 1989, p. 291-299. | MR | Zbl

[M] Mosco (U.). - Composite media and asymptotic Dirichlet form, J. Funct. Anal., t. 123, 1994, p. 368-421. | MR | Zbl

[Osh] Oshima (Y.). - On conservativeness and recurrence criteria for Markov processes, Potential Analysis, t. 1, 1992, p. 115-131. | MR | Zbl

[Ok1] Ôkura (H.). - Recurrence criteria for skew products of symmetric Markov processes, Forum Math., t. 1, 1989, p. 331-357. | EuDML | MR | Zbl

[Ok2] Ôkura (H.). - On the invariant sets and the irreducibility of symmetric Markov processes, in Proc 6th USSR-Japan Symp. on Probability Theory and Mathematical Statistics, World Scientific, 1992. | MR | Zbl

[Ok3] Ôkura (H.). - Capacitary inequalities and global properties of symmetric Dirichlet forms, preprint. | MR | Zbl

[Sto1] Stoll (W.). - The growth of the area of a transcendental analytic set I, Math. Annalen, t. 156, 1964, p. 47-78. | EuDML | MR | Zbl

[Sto2] Stoll (W.). - The growth of the area of a transcendental analytic set II, Math. Annalen, t. 156, 1964, p. 144-170. | EuDML | MR | Zbl

[Stu1] Sturm (K.T.). - Analysis on local Dirichlet spaces I. Reccurence, consevativeness and Lp-Liouville properties, J. reine angew. Math., t. 456, 1994, p. 173-196. | EuDML | MR | Zbl

[Stu2] Sturm (K.T.). - Sharp estimates for capacities and applications to symmetric diffusions, preprint. | MR | Zbl

[S-W] Sibony (N.) and Wong (P.M.). - Some remarks on the Casorati-Weierstrass'theorem, Ann. Polon. Math., t. 39, 1981, p. 165-174. | EuDML | MR | Zbl

[T1] Takegoshi (K.). - A Liouville theorem on an analytic space, J. Math. Soc. Japan, t. 45, 1993, p. 301-311. | MR | Zbl

[T2] Takegoshi (K.). - Energy estimates and Liouville theorems for harmonic maps, Ann. École Norm. Sup., t. 23, 1990, p. 563-592. | EuDML | Numdam | MR | Zbl

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