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Volumn 132, Issue 9, 2004, Pages 2629-2638

Spectral gap for hyperbounded operators

Author keywords

Ergodicity; Hyperboundedness; Log Sobolev inequality; Spectral gap

Indexed keywords


EID: 4344568074     PISSN: 00029939     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0002-9939-04-07414-3     Document Type: Article
Times cited : (10)

References (21)
  • 1
    • 0001332868 scopus 로고    scopus 로고
    • Uniform positivity improving property, Sobolev inequalities, and spectral gaps
    • MR 2000d:60125
    • S. Aida, Uniform positivity improving property, Sobolev inequalities, and spectral gaps, J. Funct. Anal. 158 (1998), 152-185. MR 2000d:60125
    • (1998) J. Funct. Anal. , vol.158 , pp. 152-185
    • Aida, S.1
  • 2
    • 0002432396 scopus 로고    scopus 로고
    • On Sobolev and logarithmic Sobolev inequalities for Markov semigroups
    • (K. D. Elworthy, S. Kusuoka and I. Shigekawa, eds.), World Scientific. MR 99m:60110
    • D. Bakry, On Sobolev and logarithmic Sobolev inequalities for Markov semigroups, in "New Trends in Stochastic Analysis" (K. D. Elworthy, S. Kusuoka and I. Shigekawa, eds.), pp. 43-75, World Scientific, 1997. MR 99m:60110
    • (1997) New Trends in Stochastic Analysis , pp. 43-75
    • Bakry, D.1
  • 3
    • 0000573290 scopus 로고
    • Ultracontractivity and the heat kernel for Schrödinger operators and dirichlet laplacians
    • MR 86e:47054
    • E. B. Davies and B. Simon, Ultracontractivity and the heat kernel for Schrödinger operators and Dirichlet Laplacians, J. Funct. Anal. 59 (1984), 335-395. MR 86e:47054
    • (1984) J. Funct. Anal. , vol.59 , pp. 335-395
    • Davies, E.B.1    Simon, B.2
  • 4
    • 0003341571 scopus 로고
    • Large deviations
    • Academic Press, San Diego. MR 90h:60026
    • J. D. Deuschel and D. Stroock, Large Deviations, Pure and Appl. Math. Ser. 137, Academic Press, San Diego, 1989. MR 90h:60026
    • (1989) Pure and Appl. Math. Ser. , vol.137
    • Deuschel, J.D.1    Stroock, D.2
  • 5
    • 0036109823 scopus 로고    scopus 로고
    • Functional inequalities for uniformly integrable semigroups and application to essential spectrums
    • MR 2003a:47097
    • F.-Z. Gong and F.-Y. Wang, Functional inequalities for uniformly integrable semigroups and application to essential spectrums, Forum Math. 14 (2002), 293-313. MR 2003a:47097
    • (2002) Forum Math. , vol.14 , pp. 293-313
    • Gong, F.-Z.1    Wang, F.-Y.2
  • 6
    • 0034670469 scopus 로고    scopus 로고
    • Spectral gap of positive operators and applications
    • MR 2002a:47057
    • F. Gong and L. Wu, Spectral gap of positive operators and applications, C. R. Acad. Sci. Paris Sér. I Math. 331 (2000), 983-988. MR 2002a:47057
    • (2000) C. R. Acad. Sci. Paris Sér. I Math. , vol.331 , pp. 983-988
    • Gong, F.1    Wu, L.2
  • 7
    • 0001429116 scopus 로고
    • Logarithmic Sobolev inequalities
    • MR 54:8263
    • L. Gross, Logarithmic Sobolev inequalities, Amer. J. Math. 97 (1975), 1061-1083. MR 54:8263
    • (1975) Amer. J. Math. , vol.97 , pp. 1061-1083
    • Gross, L.1
  • 8
    • 0002236459 scopus 로고
    • Logarithmic Sobolev inequalities and contractivity properties of semigroups
    • Springer-Verlag, Berlin. MR 95h:47061
    • L. Gross, Logarithmic Sobolev inequalities and contractivity properties of semigroups, Lecture Notes in Math., vol. 1563, 54-88, Springer-Verlag, Berlin, 1993. MR 95h:47061
    • (1993) Lecture Notes in Math. , vol.1563 , pp. 54-88
    • Gross, L.1
  • 9
    • 0006806919 scopus 로고    scopus 로고
    • p
    • p, Osaka J. Math. 37 (2000), 603-624; 39 (2002), 771. MR 2001k: 60109; MR 2003h:60112
    • (2000) Osaka J. Math. , vol.37 , pp. 603-624
    • Hino, M.1
  • 10
    • 0036763114 scopus 로고    scopus 로고
    • MR 2001k:60109; MR 2003h:60112
    • p, Osaka J. Math. 37 (2000), 603-624; 39 (2002), 771. MR 2001k: 60109; MR 2003h:60112
    • (2002) Osaka J. Math. , vol.39 , pp. 771
  • 11
    • 0002445127 scopus 로고
    • Analysis on wiener spaces II: Differential forms
    • MR 93c:58230
    • S. Kusuoka, Analysis on Wiener spaces II: differential forms, J. Funct. Anal. 103 (1992), 229-274. MR 93c:58230
    • (1992) J. Funct. Anal. , vol.103 , pp. 229-274
    • Kusuoka, S.1
  • 12
    • 0003737306 scopus 로고
    • North-Holland, Amsterdam. MR 54:3852
    • D. Revuz, Markov Chains, North-Holland, Amsterdam, 1976. MR 54:3852
    • (1976) Markov Chains
    • Revuz, D.1
  • 13
    • 0035485240 scopus 로고    scopus 로고
    • 2-convergence rates of Markov semigroups
    • MR 2002j:47075
    • 2-convergence rates of Markov semigroups, J. Funct. Anal. 185 (2001), 564-603. MR 2002j:47075
    • (2001) J. Funct. Anal. , vol.185 , pp. 564-603
    • Röckner, M.1    Wang, F.-Y.2
  • 14
    • 0000247778 scopus 로고
    • Diffusion on compact Riemannian manifolds and logarithmic Sobolev inequalities
    • MR 83f:58080a
    • O. S. Rothaus, Diffusion on compact Riemannian manifolds and logarithmic Sobolev inequalities, J. Funct. Anal. 42 (1981), 102-109. MR 83f:58080a
    • (1981) J. Funct. Anal. , vol.42 , pp. 102-109
    • Rothaus, O.S.1
  • 15
    • 84966240844 scopus 로고
    • A remark on Nelson's best hypercontractive estimates
    • MR 53:4825
    • B. Simon, A remark on Nelson's best hypercontractive estimates, Proc. Amer. Math. Soc. 55 (1976), 376-378. MR 53:4825
    • (1976) Proc. Amer. Math. Soc. , vol.55 , pp. 376-378
    • Simon, B.1
  • 16
    • 0001093583 scopus 로고
    • Hypercontractive semigroups and two dimensional self-coupled base fields
    • MR 45:2528
    • B. Simon and R. Høegh-Krohn, Hypercontractive semigroups and two dimensional self-coupled Base fields, J. Funct. Anal. 9 (1972), 121-180. MR 45:2528
    • (1972) J. Funct. Anal. , vol.9 , pp. 121-180
    • Simon, B.1    Høegh-Krohn, R.2
  • 17
    • 0034419013 scopus 로고    scopus 로고
    • Functional inequalities, semigroup properties and spectrum estimates
    • MR 2002b:47083
    • F.-Y. Wang, Functional inequalities, semigroup properties and spectrum estimates, Infin. Dimen. Anal. Quantum Probab. Relat. Topics 3 (2000), 263-295. MR 2002b:47083
    • (2000) Infin. Dimen. Anal. Quantum Probab. Relat. Topics , vol.3 , pp. 263-295
    • Wang, F.-Y.1
  • 18
    • 0037209578 scopus 로고    scopus 로고
    • Functional inequalities for the decay of sub-Markov semigroups
    • MR 2004a:47051
    • F.-Y. Wang, Functional inequalities for the decay of sub-Markov semigroups, Potential Analysis 18 (2003), 1-23. MR 2004a:47051
    • (2003) Potential Analysis , vol.18 , pp. 1-23
    • Wang, F.-Y.1
  • 19
    • 0000038655 scopus 로고    scopus 로고
    • Uniformly integrable operators and large deviations for Markov processes
    • MR 2001e:60062
    • L. Wu, Uniformly integrable operators and large deviations for Markov processes, J. Funct. Anal. 172 (2000), 301-376. MR 2001e:60062
    • (2000) J. Funct. Anal. , vol.172 , pp. 301-376
    • Wu, L.1
  • 20
    • 0842346774 scopus 로고    scopus 로고
    • Essential spectral radius for Markov semigroups (I): Discrete time case
    • L. Wu, Essential spectral radius for Markov semigroups (I): discrete time case, Probab. Theory Relat. Fields 128 (2004), 255-321.
    • (2004) Probab. Theory Relat. Fields , vol.128 , pp. 255-321
    • Wu, L.1
  • 21
    • 0004021335 scopus 로고
    • Functional analysis, sixth edition
    • Springer-Verlag, Berlin. MR 82i:46002
    • K. Yosida, Functional Analysis, sixth edition, Grundlehren der Mathematischen Wissenschaften, band 123, Springer-Verlag, Berlin, 1980. MR 82i:46002
    • (1980) Grundlehren der Mathematischen Wissenschaften , vol.123
    • Yosida, K.1


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