Spectral gap of positive operators and applications

Journal des Mathematiques Pures et Appliquees

Volumn 85, Issue 2, 2006, Pages 151-191

  Gong, Fuzhou ^a   Wu, Liming ^b,c  

^a INSTITUTE OF APPLIED MATHEMATICS   (China)

^b UNIVERSITÉ BLAISE PASCAL   (France)

^c WUHAN UNIVERSITY   (China)

Author keywords

Positive operator; Spectral gap (or Poincar inequality); Tail norm; Uniform positive improvingness

Indexed keywords

EID: 31644440265     PISSN: 00217824     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.matpur.2004.11.004     Document Type: Article

References (35)

1. S. Aida Uniform positivity improving property, Sobolev inequality and spectral gaps J. Funct. Anal. 158 1998 152-185
2. S. Aida An estimate of the gap of spectrum of Schrödinger operators which generate hyperbounded semigroups J. Funct. Anal. 185 2001 474-526
3. W. Arendt et al. in: R. Nager ed. One Parameter Semigroups of Positive Operators Lecture Notes in Math. vol. 1184 1986 Springer-Verlag Berlin/ New York
4. D. Bakry L'hypercontractivité et son utilisation en théorie des semigroupes in: École d'Été de Probabilités de Saint-Flour (1992) in: Lecture Notes in Math. vol. 1581 1994 Springer-Verlag Berlin/New York
5. D. Bakry Z.M. Qian D. Bakry Z.M. Qian Some new results on eigenvectors via dimension, diameter, and Ricci curvature Adv. in Math. 155 2000 98-153
6. M.F. Chen Eigenvalues, Inequalities and Ergodic Theory (collection of papers) 2000 Peking Normal University Press
7. F.Z. Gong L.M. Wu Spectral gap of positive operators and applications C. R. Acad. Sci. Paris Sér. 1 331 2000 983-988
8. F.Z. Gong M. Röckner L.M. Wu Poincaré inequality for weighted first order Sobolev spaces on loop spaces J. Funct. Anal. 185 2001 527-563
9. F.Z. Gong F.Y. Wang Functional inequalities for uniformly integrable semigroups and application to essential spectrum Forum Math. 14 2002 293-313
10. L. Gross Existence and uniqueness of physical ground states J. Funct. Anal. 10 1972 52-109
11. L. Gross Logarithmic Sobolev inequalities Amer. J. Math. 97 1975 1061-1083
12. M. Hino Spectral properties of Laplacians on an abstract Wiener space with a weighted Wiener measure J. Funct. Anal. 147 1997 485-520
13. p Osaka J. Math. 37 2000 603-624
14. S. Kusuoka Analysis on Wiener spaces II: Differential forms J. Funct. Anal. 103 1992 229-274
15. M. Ledoux Concentration of measure and logarithmic Sobolev inequalities in: Séminaire de Probabilités XXXIII in: Lecture Notes in Math. vol. 1709 1999 Springer-Verlag Berlin/New York 120-216
16. Z.M. Ma M. Röckner Introduction to the Theory of (Non-Symmetric) Dirichlet Forms 1992 Springer-Verlag Berlin/Heidelberg/New York
17. P. Mattieu in: Quand l'inégalité log-Sobolev implique l'inégalité de trou spectral Séminaire de Probabilités XXXII in: Lecture Notes in Math. vol. 1686 1998 Springer-Verlag Berlin/New York 30-35
18. P. Meyer-Nieberg Banach Lattices 1991 Springer-Verlag Berlin/New York
19. S.P. Meyn R.L. Tweedie Markov Chains and Stochastic Stability 1993 Springer-Verlag Berlin/New York
20. E. Nelson A quartic interaction in two dimensions in: R. Goodman I. Segal eds. Mathematical Theory of Elementary Particles 1966 MIT Press Cambridge, MA
21. E. Nummelin General Irreducible Markov Chains and Non-Negative operators Cambridge Tracts in Math. vol. 83 1984 Cambridge Univ. Press Cambridge, UK
22. B. de Pagter A.R. Schep Measures of non-compactness of operators in Banach lattices J. Funct. Anal. 78 1988 31-55
23. M. Reed B. Simon Methods of Modern Mathematical Physics, II, Fourier Analysis, Self-adjointness 1975 Academic Press San Diego, CA
24. D. Revuz Markov Chains 1976 North-Holland Amsterdam
25. M. Saloff-Coste Lectures on finite Markov chains in: École d'Été de Probabilités de Saint-Flour 1996 in: Lecture Notes in Math. vol. 1685 1997 Springer-Verlag Berlin/New York 301-413
26. H.H. Schaefer Banach Lattices and Positive Operators 1974 Springer-Verlag Berlin/New York
27. B. Simon R. Hoegh-Krohn Hypercontractive semigroups and two-dimensional self-coupled Bose fields J. Funct. Anal. 9 1972 121-180
28. F.Y. Wang, Spectral gap for hyperbounded operators, Preprint, 2002, Proc. Amer. Math. Soc., submitted for publication
29. L.W. Weis On the computation of some quantities in the theory of Fredholm operators in: Proceedings of 12th Winter School on Abstract Analysis Srni, 1984 Rendiconti de Circolo Mathematico di Palermo, Ser. II 5 Supplemento 1984
30. L.M. Wu Large deviations for Markov processes under superboundedness C. R. Acad. Sci. Paris Sér. I 321 1995 777-782
31. L.M. Wu Moderate deviations of dependent random variables related to CLT Ann. Probab. 23 1995 420-445
32. L.M. Wu Uniformly integrable operators and large deviations for Markov processes J. Funct. Anal. 172 2000 301-376
33. L.M. Wu Essential spectral radius for Markov semigroups (I): Discrete time case Probab. Theory Relat. Fields 128 2004 255-321
34. L.M. Wu, Uniform positive improvingness, tail norm and spectral gap, Preprint, 2002
35. K. Yosida Functional Analysis 1978 Springer-Verlag Berlin/New York