Integrated density of states of self-similar Sturm-Liouville operators and holomorphic dynamics in higher dimension

Annales de l'institut Henri Poincare (B) Probability and Statistics

Volumn 37, Issue 3, 2001, Pages 275-311

  Sabot, Christophe ^a  

^a SORBONNE UNIVERSITÉ   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0042334598     PISSN: 02460203     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0246-0203(00)01068-2     Document Type: Article

References (28)

1. Barlow M.T. Diffusions on Fractals. St Flour Lecture Notes 1995. 1998.
2. Barlow M.T., Kigami J. Localized eigenfunctions of the Laplacian on p.c.f. self-similar sets. J. Lond. Math. Soc. 56:(2):1997;320-332.
3. Carmona R., Lacroix J. Spectral Theory of Random Schrödinger Operators. Probabilities and Applications. 1990;Birkhaüser, Boston.
4. Forman R. Functional determinants and geometry. Invent. Math. 88:1987;447-493.
5. Forman R. Determinants, finite-difference operators and boundary value problems. Comm. Math. Phys. 147:1992;485-526.
6. Fornæss J.E. Dynamics in Several Complex Variables. CBMS, Regional Conference Series in Math., No. 87. 1996;Amer. Math. Soc.
7. Fornæss J.E., Sibony N. Complex dynamics in higher dimension. I. Complex Analytic Methods in Dynamical Systems (Rio de Janeiro, 1992). Astérisque, 222. 1994;201-231.
8. Fornæss J.E., Sibony N. Complex dynamics in higher dimension. II. Modern Methods in Complex Analysis. Ann. Math. Studies, 137. 1995;135-182 University Press, Princeton, NJ.
9. Fukushima M., Oshima Y., Takeda M. Dirichlet Forms and Symmetric Markov Processes. de Gruyter Stud. Math. 19. 1994;Walter de Gruyter, Berlin, New York.
10. Fukushima M. Dirichlet forms, diffusion processes and spectral dimensions for nested fractals. Albevario S., et al. Ideas and Methods in Mathematical Analysis, Stochastics and Applications, Proc. Conf. in Memory of Hoegh-Krohn, Vol. 1. 1993;151-161 Cambridge Univ. Press, Cambridge.
11. Fukushima M., Shima T. On the spectral analysis for the Sierpinski gasket. Potential Analysis. 1:1992;1-35.
12. Fukushima M., Shima T. On the discontinuity and tail behaviours of the integrated density of states for nested pre-fractals. Comm. Math. Phys. 163:1994;461-471.
13. Hörmander L. Notions of Convexity. Progress in Mathematics. 127:1994;Birkhäuser.
14. Kigami J. Harmonic calculus on p.c.f. self-similar sets. Trans. Am. Math. Soc. 335:1993;721-755.
15. Kigami J. Distributions of localized eigenvalues on post critically finite self-similar sets. J. Funct. Anal. 159:1998;170-198.
16. Kigami J., Lapidus M.L. Weyl's problem for the spectral distribution of Laplacians on p.c.f. self-similar fractals. Comm. Math. Phys. 158:(1):1993;93-125.
17. Kusuoka S., Lecture on diffusion processes on nested fractals, in: Lecture Notes in Math., Vol. 1567, Springer.
18. Lapidus M.L. Analysis on fractals, Laplacians on self-similar sets, non-commutative geometry and spectral dimensions. Topological Methods in Nonlinear Analysis. 4:(1):1994;137-195.
19. Le Jan Y. Mesures associées à une forme de Dirichlet. Applications. Bull. Soc. Math. de France. 106:1978;61-112.
20. Lindstrøm T. Brownian motion on nested fractals. Mem. Amer. Math. Soc. 420:1990.
21. Pastur L., Figotin A. Spectra of Random and Almost-Periodic Operators. Grundlehren der mathematischen Wissenschaften. 297:1992;Springer-Verlag, Berlin, Heidelberg.
22. Rammal R. Spectrum of harmonic excitations on fractals. J. de Physique. 45:1984;191-206.
23. Rammal R., Toulouse G. J. Phys. Lett. 44:1983;L-13.
24. Rudin X. Real and Complex Analysis. McGraw-Hill Series in Higher Mathematics. 1966;McGraw-Hill, NY.
25. Sabot C. Existence and uniqueness of diffusions on finitely ramified self-similar fractals. Ann. Scient. Ec. Norm. Sup., 4ème série. 30:1997;605-673.
26. k : the example of the interval [0,1] , Comptes Rendus à l'Académie des Sciences, to appear.
27. k , preprint.
28. Steinmetz N. Rational Iteration. de Gruyter Studies in Mathematics. 16:1993;W. de Gruyter, Berlin.