Harmonic analysis on fractal spaces
Séminaire Bourbaki : volume 1991/92, exposés 745-759, Astérisque, no. 206 (1992), Talk no. 755, p. 345-368
@incollection{SB_1991-1992__34__345_0,
     author = {Barlow, Martin T.},
     title = {Harmonic analysis on fractal spaces},
     booktitle = {S\'eminaire Bourbaki : volume 1991/92, expos\'es 745-759},
     author = {Collectif},
     series = {Ast\'erisque},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {206},
     year = {1992},
     note = {talk:755},
     pages = {345-368},
     zbl = {0798.58079},
     mrnumber = {1206073},
     language = {en},
     url = {http://www.numdam.org/item/SB_1991-1992__34__345_0}
}
Barlow, Martin. Harmonic analysis on fractal spaces, in Séminaire Bourbaki : volume 1991/92, exposés 745-759, Astérisque, no. 206 (1992), Talk no. 755, pp. 345-368. http://www.numdam.org/item/SB_1991-1992__34__345_0/

[B1] M. T. Barlow: Random walks, electrical resistance and nested fractals. To appear in Asymptotic Problems in Probability Theory, ed. K.D. Elworthy, N. Ikeda, Pitman. | MR 1354153 | Zbl 0791.60097

[BB1] M. T. Barlow and R. F. Bass: The construction of Brownian motion on the Sierpinski carpet. Ann. Inst. H. Poincaré 25 (1989) 225-257. | Numdam | MR 1023950 | Zbl 0691.60070

[BB2] M. T. Barlow and R. F. Bass: On the resistance of the Sierpinski carpet. Proc. R. Soc. London A. 431 (1990) 345-360. | MR 1080496 | Zbl 0729.60108

[BB3] M. T. Barlow and R. F. Bass: Transition densities for Brownian motion on the Sierpinski carpet. Probab. Th. Rel. Fields 91 (1992) 307-330. | MR 1151799 | Zbl 0739.60071

[BP] M. T. Barlow and E. A. Perkins: Brownian motion on the Sierpinski gasket. Probab. Th. Rel. Fields 79 (1988) 543-623. | MR 966175 | Zbl 0635.60090

[CKS] E. A. Carlen, S. Kusuoka and D. W. Stroock: Upper bounds for symmetric Markov transition functions. Ann. Inst. H. Poincaré Sup no. 2 (1987) 245-287. | Numdam | MR 898496 | Zbl 0634.60066

[C] A. K. Chandra, P. Raghaven, W. L. Ruzzo, R. Smolensky, P. Tiwari: The electrical resistance of a graph captures its commute and cover times. Proceedings of the 21st ACM Symposium on theory of computing, 1989.

[Ch] I. Chavel: Eigenvalues in Riemannian Geometry. Academic Press, 1984. | MR 768584 | Zbl 0551.53001

[F1] M. Fukushima: Dirichlet forms and Markov processes, North Holland 1980. | MR 569058 | Zbl 0422.31007

[F2] M. Fukushima: Dirichlet forms, diffusion processes, and spectral dimensions for nested fractals. To appear in "Ideas and methods in stochastic analysis, stochastics and applications" , ed. S Albeverio et. al., Cambridge Univ. Press., Cambridge. | MR 1190496 | Zbl 0764.60081

[FS] M. Fukushima and T. Shima: On a spectral analysis for the Sierpinski gasket. To appear J. of Potential Analysis. | MR 1245223 | Zbl 1081.31501

[G] S. Goldstein: Random walks and diffusion on fractals. In: Kesten, H. (ed.) Percolation theory and ergodic theory of infinite particle systems (IMA Math. Appl., vol.8.) Springer, New York, 1987, pp.121- 129. | MR 894545 | Zbl 0621.60073

[HHW] K. Hattori, T. Hattori and H. Watanabe: Gaussian field theories and the spectral dimensions. Prog. Th. Phys. Supp. No. 92 (1987) 108-143.

[Kig1] J. Kigami: A harmonic calculus on the Sierpinski space. Japan J. Appl. Math. 6 (1989) 259-290. | MR 1001286 | Zbl 0686.31003

[Kig2] J. Kigami: A harmonic calculus for p.c.f. self-similar sets. To appear Trans. A.M.S. | MR 1076617 | Zbl 0773.31009

[Kum] T. Kumagai: Estimates of the transition densities for Brownian motion on nested fractals. Preprint 1991. | MR 1227032

[K1] S. Kusuoka: A diffusion process on a fractal. In: Ito, K., N. Ikeda, N. (ed.) Symposium on Probabilistic Methods in Mathematical Physics, Taniguchi, Katata. Academic Press, Amsterdam, 1987, pp.251-274 | MR 933827 | Zbl 0645.60081

[K2] S. Kusuoka: Dirichlet forms on fractals and products of random matrices. Publ. RIMS Kyoto Univ., 25 (1989) 659-680. | MR 1025071 | Zbl 0694.60071

[KZ] S. Kusuoka and X. Y. Zhou: Dirichlet form on fractals: Poincaré constant and resistance. Probab. Th. Rel. Fields 93, (1992) 169- 186. | MR 1176724 | Zbl 0767.60076

[L] T. Lindstrøm: Brownian motion on nested fractals. Mem. A.M.S. 420, 1990. | MR 988082 | Zbl 0688.60065

[O] H. Osada: Isoperimetric dimension and estimates of heat kernels of pre-Sierpinski carpets. Probab. Th. Rel. Fields 86 (1990) 469-490. | MR 1074740 | Zbl 0685.60081

[RT] R. Rammal and G. Toulouse: Random walks on fractal structures and percolation' clusters, J. Physique Lettres 44 (1983) L13- L22.

[S] T. Shima: On eigenvalue problems for the random walk on the Sierpinski pre-gaskets. Japan J. Appl. Ind. Math., 8 (1991) 127-142. | MR 1093832 | Zbl 0715.60088

[V] N. Th. Varopoulos: Isoperimetric inequalities and Markov chains. J. Funct. Anal. 63 (1985) 215-239. | MR 803093 | Zbl 0573.60059