Liouville theorems based on symmetric diffusions
Bulletin de la Société Mathématique de France (1996)
- Volume: 124, Issue: 4, page 545-557
- ISSN: 0037-9484
Access Full Article
topHow to cite
topKaneko, Hiroshi. "Liouville theorems based on symmetric diffusions." Bulletin de la Société Mathématique de France 124.4 (1996): 545-557. <http://eudml.org/doc/87750>.
@article{Kaneko1996,
author = {Kaneko, Hiroshi},
journal = {Bulletin de la Société Mathématique de France},
keywords = {regular strongly local Dirichlet forms; Liouville properties; Hellinger integral; subharmonic functions},
language = {eng},
number = {4},
pages = {545-557},
publisher = {Société mathématique de France},
title = {Liouville theorems based on symmetric diffusions},
url = {http://eudml.org/doc/87750},
volume = {124},
year = {1996},
}
TY - JOUR
AU - Kaneko, Hiroshi
TI - Liouville theorems based on symmetric diffusions
JO - Bulletin de la Société Mathématique de France
PY - 1996
PB - Société mathématique de France
VL - 124
IS - 4
SP - 545
EP - 557
LA - eng
KW - regular strongly local Dirichlet forms; Liouville properties; Hellinger integral; subharmonic functions
UR - http://eudml.org/doc/87750
ER -
References
top- [B-H] BOULEAU (N.) and HIRSCH (F.). — Dirichlet forms and Analysis on Wiener space. — Walter de Gruyter, Berlin, 1991. Zbl0748.60046MR93e:60107
- [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. Zbl0760.49004MR93c:35028
- [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. Zbl0312.53031MR52 #6608
- [F1] FUKUSHIMA (M.). — On holomorphic diffusions and plurisubharmonic functions, Contemporary Math, t. 78, 1988. Zbl0658.60105MR89g:60237
- [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. Zbl0637.32013MR88m:32033
- [F-O-T] FUKUSHIMA (M.), OSHIMA (M.) and TAKEDA (M.). — Dirichlet forms and symmetric Markov processes. — Walter de Gruyter, Berlin, 1994. Zbl0838.31001
- [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. Zbl43.0421.03JFM43.0421.03
- [K] KANEKO (H.). — A stochastic approach to a Liouville property for plurisubharmonic functions, J. Math. Soc. Japan, t. 41, 1989, p. 291-299. Zbl0681.32015MR90b:32032
- [M] MOSCO (U.). — Composite media and asymptotic Dirichlet form, J. Funct. Anal., t. 123, 1994, p. 368-421. Zbl0808.46042MR95d:47088
- [Osh] OSHIMA (Y.). — On conservativeness and recurrence criteria for Markov processes, Potential Analysis, t. 1, 1992, p. 115-131. Zbl1081.60545MR94k:60118
- [Ok1] ÔKURA (H.). — Recurrence criteria for skew products of symmetric Markov processes, Forum Math., t. 1, 1989, p. 331-357. Zbl0686.60079MR91a:60194
- [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. Zbl0818.60069MR94k:31012
- [Ok3] ÔKURA (H.). — Capacitary inequalities and global properties of symmetric Dirichlet forms, preprint. Zbl0840.60071
- [Sto1] STOLL (W.). — The growth of the area of a transcendental analytic set I, Math. Annalen, t. 156, 1964, p. 47-78. Zbl0126.09502MR29 #3670
- [Sto2] STOLL (W.). — The growth of the area of a transcendental analytic set II, Math. Annalen, t. 156, 1964, p. 144-170. Zbl0126.09502MR29 #3670
- [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. Zbl0806.53041MR95i:31003
- [Stu2] STURM (K.T.). — Sharp estimates for capacities and applications to symmetric diffusions, preprint. Zbl0828.60062
- [S-W] SIBONY (N.) and WONG (P.M.). — Some remarks on the Casorati-Weierstrass'theorem, Ann. Polon. Math., t. 39, 1981, p. 165-174. Zbl0476.32005MR82k:32015
- [T1] TAKEGOSHI (K.). — A Liouville theorem on an analytic space, J. Math. Soc. Japan, t. 45, 1993, p. 301-311. Zbl0788.32004MR94b:32040
- [T2] TAKEGOSHI (K.). — Energy estimates and Liouville theorems for harmonic maps, Ann. École Norm. Sup., t. 23, 1990, p. 563-592. Zbl0718.58018MR91j:58047
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.