Spectral gaps on loop spaces: A counterexample;Trous spectraux sur les espaces de lacets: Un contre-exemple

Comptes Rendus de l'Academie des Sciences - Series I: Mathematics

Volumn 330, Issue 3, 2000, Pages 237-242

  Eberle, Andreas ^a,b  

^a BIELEFELD UNIVERSITY   (Germany)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034134530     PISSN: 07644442     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0764-4442(00)00141-5     Document Type: Article

References (11)

1. [1] Aida S., Differential calculus on path and loop spaces. II. Irredubility of Dirichlet forms on loop spaces, Bull. Sci. Math. 122 (1998) 635-666.
2. [2] Capitaine M., Hsu E.P., Ledoux M., Martingale representation and a simple proof of logarithmic Sobolev inequalities on path spaces, Electron. Comm. Probab. 2 (1997) 71-81.
3. [3] Davies E.B., Heat Kernels and Spectral Theory, Cambridge University Press, Cambridge, 1990.
4. [4] Driver B., A Cameron-Martin type quasi-invariance theorem for pinned Brownian motion on a compact Riemannian manifold, Trans. Amer. Math. Soc. 342 (1994) 375-395.
5. [5] Driver B., Röckner M., Construction of diffusions on path and loop spaces of compact Riemannian manifolds, C. R. Acad. Sci. Paris 315 Série I (1992) 603-608.
6. [6] Eberle A., Diffusions on path and loop spaces: existence, finite-dimensional approximation and Hölder continuity, Probab. Theory Related Fields 109 (1997) 77-99.
7. [7] Eberle A., On the absence of spectral gaps on certain loop spaces, (in preparation).
8. [8] Fang S., Inégalité du type de Poincaré sur l'espace des chemins riemanniens, C. R. Acad. Sci. Paris 318 Série I (1994) 257-260.
9. [9] Kazumi T., Le processus d'Ornstein-Uhlenbeck sur l'espace des chemins riemanniens et le problème des martingales, J. Funct. Anal. 144 (1997) 20-45.
10. [10] Malliavin P., Stochastic Analysis, Springer-Verlag, Berlin, 1997.
11. [11] Spivak M., A Comprehensive Introduction to Differential Geometry, Vol. III, Second edition, Publish or Perish, Inc., Wilmington, Del., 1979.