@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/} }
TY - JOUR AU - Sabot, Christophe TI - Integrated density of states of self-similar Sturm-Liouville operators and holomorphic dynamics in higher dimension JO - Annales de l'I.H.P. Probabilités et statistiques PY - 2001 SP - 275 EP - 311 VL - 37 IS - 3 PB - Elsevier UR - http://www.numdam.org/item/AIHPB_2001__37_3_275_0/ LA - en ID - AIHPB_2001__37_3_275_0 ER -
%0 Journal Article %A Sabot, Christophe %T Integrated density of states of self-similar Sturm-Liouville operators and holomorphic dynamics in higher dimension %J Annales de l'I.H.P. Probabilités et statistiques %D 2001 %P 275-311 %V 37 %N 3 %I Elsevier %U http://www.numdam.org/item/AIHPB_2001__37_3_275_0/ %G en %F AIHPB_2001__37_3_275_0
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, Tome 37 (2001) no. 3, pp. 275-311. http://www.numdam.org/item/AIHPB_2001__37_3_275_0/
[1] Diffusions on Fractals, St Flour Lecture Notes 1995, 1998. | MR | Zbl
,[2] Localized eigenfunctions of the Laplacian on p.c.f. self-similar sets, J. Lond. Math. Soc. 56 (2) (1997) 320-332. | MR | Zbl
, ,[3] Spectral Theory of Random Schrödinger Operators, Probabilities and Applications, Birkhaüser, Boston, 1990. | MR | Zbl
, ,[4] Functional determinants and geometry, Invent. Math. 88 (1987) 447-493. | EuDML | MR | Zbl
,[5] Determinants, finite-difference operators and boundary value problems, Comm. Math. Phys. 147 (1992) 485-526. | MR | Zbl
,[6] Dynamics in Several Complex Variables, CBMS, Regional Conference Series in Math., No. 87, Amer. Math. Soc, 1996. | MR | Zbl
,[7] 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] 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] Dirichlet Forms and Symmetric Markov Processes, de Gruyter Stud. Math. 19, Walter de Gruyter, Berlin, New York, 1994. | MR | Zbl
, , ,[10] Dirichlet forms, diffusion processes and spectral dimensions for nested fractals, in: , (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] On the spectral analysis for the Sierpinski gasket, Potential Analysis 1 (1992) 1-35. | MR | Zbl
, ,[12] 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] Notions of Convexity, Progress in Mathematics, 127, Birkhäuser, 1994. | MR | Zbl
,[14] Harmonic calculus on p.c.f. self-similar sets, Trans. Am. Math. Soc. 335 (1993) 721-755. | MR | Zbl
,[15] Distributions of localized eigenvalues on post critically finite self-similar sets, J. Funct. Anal. 159 (1998) 170-198. | MR | Zbl
,[16] 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] 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] Mesures associées à une forme de Dirichlet. Applications, Bull. Soc. Math. de France 106 (1978) 61-112. | Numdam | MR | Zbl
,[20] Brownian motion on nested fractals, Mem. Amer. Math. Soc. 420 (1990). | MR | Zbl
,[21] Spectra of Random and Almost-Periodic Operators, Grundlehren der mathematischen Wissenschaften, 297, Springer-Verlag, Berlin, Heidelberg, 1992. | MR | Zbl
, ,[22] Spectrum of harmonic excitations on fractals, J. de Physique 45 (1984) 191-206. | MR
,[23] J. Phys. Lett. 44 (1983) L-13.
, ,[24] Real and Complex Analysis, McGraw-Hill Series in Higher Mathematics, McGraw-Hill, NY, 1966. | MR | Zbl
,[25] 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] Rational Iteration, de Gruyter Studies in Mathematics, 16, W. de Gruyter, Berlin, 1993. | MR | Zbl
,