Integrated density of states of self-similar Sturm-Liouville operators and holomorphic dynamics in higher dimension
Annales de l'I.H.P. Probabilités et statistiques, Volume 37 (2001) no. 3, pp. 275-311.
@article{AIHPB_2001__37_3_275_0,
author = {Sabot, Christophe},
title = {Integrated density of states of self-similar {Sturm-Liouville} operators and holomorphic dynamics in higher dimension},
journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
pages = {275--311},
publisher = {Elsevier},
volume = {37},
number = {3},
year = {2001},
zbl = {1038.37036},
language = {en},
url = {http://www.numdam.org/item/AIHPB_2001__37_3_275_0/}
}
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%A Sabot, Christophe
%T Integrated density of states of self-similar Sturm-Liouville operators and holomorphic dynamics in higher dimension
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%D 2001
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Sabot, Christophe. Integrated density of states of self-similar Sturm-Liouville operators and holomorphic dynamics in higher dimension. Annales de l'I.H.P. Probabilités et statistiques, Volume 37 (2001) no. 3, pp. 275-311. http://www.numdam.org/item/AIHPB_2001__37_3_275_0/

[1] M.T Barlow, Diffusions on Fractals, St Flour Lecture Notes 1995, 1998. | MR | Zbl

[2] M.T Barlow, J Kigami, Localized eigenfunctions of the Laplacian on p.c.f. self-similar sets, J. Lond. Math. Soc. 56 (2) (1997) 320-332. | MR | Zbl

[3] R Carmona, J Lacroix, Spectral Theory of Random Schrödinger Operators, Probabilities and Applications, Birkhaüser, Boston, 1990. | MR | Zbl

[4] R Forman, Functional determinants and geometry, Invent. Math. 88 (1987) 447-493. | EuDML | MR | Zbl

[5] R Forman, Determinants, finite-difference operators and boundary value problems, Comm. Math. Phys. 147 (1992) 485-526. | MR | Zbl

[6] J.E Fornæss, Dynamics in Several Complex Variables, CBMS, Regional Conference Series in Math., No. 87, Amer. Math. Soc, 1996. | MR | Zbl

[7] J.E Fornæss, N Sibony, Complex dynamics in higher dimension. I, in: Complex Analytic Methods in Dynamical Systems (Rio de Janeiro, 1992), Astérisque, 222, 1994, pp. 201-231. | MR | Zbl

[8] J.E Fornæss, N Sibony, Complex dynamics in higher dimension. II, in: Modern Methods in Complex Analysis, Ann. Math. Studies, 137, University Press, Princeton, NJ, 1995, pp. 135-182. | MR | Zbl

[9] M Fukushima, Y Oshima, M Takeda, Dirichlet Forms and Symmetric Markov Processes, de Gruyter Stud. Math. 19, Walter de Gruyter, Berlin, New York, 1994. | MR | Zbl

[10] M Fukushima, Dirichlet forms, diffusion processes and spectral dimensions for nested fractals, in: Albevario S, (Eds.), Ideas and Methods in Mathematical Analysis, Stochastics and Applications, Proc. Conf. in Memory of Hoegh-Krohn, Vol. 1, Cambridge Univ. Press, Cambridge, 1993, pp. 151-161. | MR | Zbl

[11] M Fukushima, T Shima, On the spectral analysis for the Sierpinski gasket, Potential Analysis 1 (1992) 1-35. | MR | Zbl

[12] M Fukushima, T Shima, On the discontinuity and tail behaviours of the integrated density of states for nested pre-fractals, Comm. Math. Phys. 163 (1994) 461-471. | MR | Zbl

[13] L Hörmander, Notions of Convexity, Progress in Mathematics, 127, Birkhäuser, 1994. | MR | Zbl

[14] J Kigami, Harmonic calculus on p.c.f. self-similar sets, Trans. Am. Math. Soc. 335 (1993) 721-755. | MR | Zbl

[15] J Kigami, Distributions of localized eigenvalues on post critically finite self-similar sets, J. Funct. Anal. 159 (1998) 170-198. | MR | Zbl

[16] J Kigami, M.L Lapidus, Weyl's problem for the spectral distribution of Laplacians on p.c.f. self-similar fractals, Comm. Math. Phys. 158 (1) (1993) 93-125. | MR | Zbl

[17] Kusuoka S., Lecture on diffusion processes on nested fractals, in: Lecture Notes in Math., Vol. 1567, Springer.

[18] M.L Lapidus, Analysis on fractals, Laplacians on self-similar sets, non-commutative geometry and spectral dimensions, Topological Methods in Nonlinear Analysis 4 (1) (1994) 137-195. | MR | Zbl

[19] Y Le Jan, Mesures associées à une forme de Dirichlet. Applications, Bull. Soc. Math. de France 106 (1978) 61-112. | Numdam | MR | Zbl

[20] T Lindstrøm, Brownian motion on nested fractals, Mem. Amer. Math. Soc. 420 (1990). | MR | Zbl

[21] L Pastur, A Figotin, Spectra of Random and Almost-Periodic Operators, Grundlehren der mathematischen Wissenschaften, 297, Springer-Verlag, Berlin, Heidelberg, 1992. | MR | Zbl

[22] R Rammal, Spectrum of harmonic excitations on fractals, J. de Physique 45 (1984) 191-206. | MR

[23] R Rammal, G Toulouse, J. Phys. Lett. 44 (1983) L-13.

[24] X Rudin, Real and Complex Analysis, McGraw-Hill Series in Higher Mathematics, McGraw-Hill, NY, 1966. | MR | Zbl

[25] C Sabot, Existence and uniqueness of diffusions on finitely ramified self-similar fractals, Ann. Scient. Ec. Norm. Sup., 4ème série 30 (1997) 605-673. | Numdam | MR | Zbl

[26] Sabot C., Density of states of diffusions on self-similar sets and holomorphic dynamics in Pk: the example of the interval [0,1], Comptes Rendus à l'Académie des Sciences, to appear. | Zbl

[27] Sibony N., Dynamique des applications rationnelles de Pk, preprint. | MR

[28] N Steinmetz, Rational Iteration, de Gruyter Studies in Mathematics, 16, W. de Gruyter, Berlin, 1993. | MR | Zbl