Functional inequalities for uniformly integrable semigroups and application to essential spectrums

Forum Mathematicum

Volumn 14, Issue 2, 2002, Pages 293-313

  Gong, Fu Zhou ^a   Wang, Feng Yu ^b  

^a BEIJING NORMAL UNIVERSITY   (China)

^b INSTITUTE OF APPLIED MATHEMATICS   (China)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0036109823     PISSN: 09337741     EISSN: None     Source Type: Journal    
DOI: 10.1515/form.2002.013     Document Type: Article

References (21)

1. Aida, S. and Kawabi, H.: Short time asymptotics of certain infinite dimensional diffusion processes. Preprint (1998)
2. Bakry, D.: L'hypercontractivité et son utilisation en théorie des semigroups. Lecture Notes in Math. 1581 (1994), 1-114
3. Bourbaki, N.: Espaces Vectoriels Topologiques (Livre V). Hermann, Paris 1955
4. p spaces. Stochastics and Stochastics Reports 59 (1996), 183-209
5. Cipriani, F.: Sobolev-Orlicz imbeddings, weak compactness and spectrum. Preprint No. 378/1999, Piazza Leonardo da Vinci
6. Deuschel, J. and Stroock, D.: Large Deviations. Academic Press, New York 1989
7. Donnely, H. and Li, P.: Pure point spectrum and negative curvature for noncompact manifolds. Duke Math. J. 46 (1979), 497-503
8. Grillo, G.: On the pearson's theorem in local Dirichlet spaces. Z. Anal. Anwendungen 17 (1998), 329-338
9. Gross, L.: Logarithmic Sobolev inequalities. Amer. J. Math. 97 (1976), 1061-1083
10. Gross, L.: Logarithmic Sobolev inequalities and contractive properties of semigroups. Lecture Notes in Math. 1563 (1993), 54-88
11. Ha, K. S.: Spectral mapping theorems for exponentially bounded C-semigroups in Banach spaces. Semigroup Forum 38 (1989), 215-221
12. Kato, T.: Perturbation Theory for Linear Operators (second Edition). Springer-Verlag, Berlin 1976
13. Ma, Z. M. and Röckner, M.: Introduction to Theory of (Non-symmetric) Dirichlet Forms. Springer-Verlag, Berlin 1992
14. Reed, M. and Simon, B.: Methods of Modern Mathematical Physics, I: Functional Analysis. New York, Academic Press 1980
15. Röckner, M. and Wang, F. Y.: Harnack inequalities for generalized Mehler semigroups and applications. Preprint (2000)
16. Rudin, W.: Functional Analysis (Second Edition). McGraw-Hill, New York 1991
17. Wang, F. Y.: Logarithmic Sobolev inequalities on noncompact Riemannian manifolds. Probability Theory Relat. Fields 109 (1997), 417-424
18. Wang, F. Y.: Sobolev type inequalities for general symmetric forms. Proc. Amer. Math. Soc. to appear
19. Wang, F. Y.: Functional inequalities for empty essential spectrum. J. Funct. Anal. 170 (2000), 219-245
20. Wu, L. M.: Large deviations for Markov processes under superboundedness. C. R. Acad. Sci. Paris Série I 324 (1995), 777-782
21. Wu, L. M.: Uniformly integrable operators and large deviations for Markov processes. J. Funct. Anal. 172 (2000), 301-376