Exponential decay of positivity preserving semigroups on LP

Osaka Journal of Mathematics

Volumn 37, Issue 3, 2000, Pages 603-624

  Hino, Masanori ^a  

^a KYOTO UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0006806919     PISSN: 00306126     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (21)

1. S. Aida: Uniform positivity improving property, Sobolev inequality and spectral gaps, J. Funct. Anal. 158 (1998), 152-185.
2. S. Aida and D. Elworthy: Differential calculus on path and loop spaces I. Logarithmic Sobolev inequalities on path spaces, C. R. Acad. Sci. Paris 321 Série I (1995), 97-102.
3. V.I. Bogachev, N. Krylov and M. Röckner: Regularity of invariant measures: the case of non-constant diffusion part, J. Funct. Anal. 138(1996), 223-242.
4. V.I. Bogachev and M. Röckner: Regularity of invariant measures on finite and infinite dimensional spaces and applications, J. Funct. Anal. 133(1995), 168-223.
5. V. Bogachev, M. Röckner, and T.S. Zhang: Existence and uniqueness of invariant measures: an approach via sectorial forms, Appl. Math. Optim. 41(2000), 87-109.
6. G. Da Prato and J. Zabczyk: Ergodicity for Infinite Dimensional Systems, Cambridge University Press, Cambridge, 1996.
7. E.B. Davies: Heat kernels and spectral theory, Cambridge University Press, Cambridge, 1989.
8. S. Fang: Inégalité du type de sur léspace des chemins riemanniens, C.R. Acad. Sci. Paris 318 Série I (1994), 257-260.
9. L. Gross: Existence and uniqueness of physical ground states, J. Funct. Anal. 10 (1972), 52-109.
10. M. Hino: Existence of invariant measures for diffusion processes on a Wiener space, Osaka J. Math. 35(1998), 717-734.
11. E.P. Hsu: Logarithmic Sobolev inequalities on path spaces, C.R. Acad. Sci. Paris 320 Série I (1995), 1009-1012.
12. E.P. Hsu: Logarithmic Sobolev inequalities on path spaces over Riemannian manifolds, Comm. Math. Phys. 189 (1997), 9-16.
13. S. Kusuoka: Analysis on Wiener spaces II: Differential forms, J. Funct. Anal. 103 (1992), 229-274.
14. Z.M. Ma and M. Röckner: Introduction to the Theory of (Non-Symmetric) Dirichlet Forms, Springer-Verlag, Berlin-Heidelberg-New York, 1992.
15. P. Mathieu: Hitting times and spectral gap inequalities, Ann. Inst. H. Poincaré Probab. Statist. 33 (1997), 437-465.
16. P. Mathieu: On the law of the hitting time of a small set by a Markov process, preprint.
17. P. Mathieu: Quand l'inegalite log-Sobolev implique l'inegalite de trou spectral, Séminaire de Prob. XXXII, 30-35, Lecture Notes in Math. vol. 1686, Springer-Verlag, Berlin-Heidelberg-New York, 1998.
18. R. Nagel (ed.): One-parameter Semigroups of Positive Operators, Lecture Notes in Math. vol. 1184, Springer-Verlag, Berlin-Heidelberg-New York, 1986.
19. I. Shigekawa: Existence of invariant measures of diffusions on an abstract Wiener space, Osaka J. Math. 24 (1987), 37-59.
20. R.v. Vintschger: The existence of invariant measures for C[0, 1]-valued diffusions, Probab. Th. Rel. Fields 82(1989), 307-313.
21. T.S. Zhang: Existence of invariant measures for diffusion processes with infinite dimensional state space, Ideas and Methods in Mathematical Analysis, Stochastics, and Applications, R. Høegh-Krohn Memorial, Vol. I, 283-294, Cambridge Univ. Press, Cambridge, UK, 1992.