Harmonic analysis on fractal spaces
Séminaire Bourbaki : volume 1991/92, exposés 745-759, Astérisque, no. 206 (1992), Exposé no. 755, 24 p.

Voir la notice du chapitre de livre provenant de la source Numdam

MR Zbl EuDML
Barlow, Martin. Harmonic analysis on fractal spaces, dans Séminaire Bourbaki : volume 1991/92, exposés 745-759, Astérisque, no. 206 (1992), Exposé no. 755, 24 p.. http://geodesic.mathdoc.fr/item/SB_1991-1992__34__345_0/
@incollection{SB_1991-1992__34__345_0,
     author = {Barlow, Martin},
     title = {Harmonic analysis on fractal spaces},
     booktitle = {S\'eminaire Bourbaki : volume 1991/92, expos\'es 745-759},
     series = {Ast\'erisque},
     note = {talk:755},
     pages = {345--368},
     year = {1992},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {206},
     mrnumber = {1206073},
     zbl = {0798.58079},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SB_1991-1992__34__345_0/}
}
TY  - CHAP
AU  - Barlow, Martin
TI  - Harmonic analysis on fractal spaces
BT  - Séminaire Bourbaki : volume 1991/92, exposés 745-759
AU  - Collectif
T3  - Astérisque
N1  - talk:755
PY  - 1992
SP  - 345
EP  - 368
IS  - 206
PB  - Société mathématique de France
UR  - http://geodesic.mathdoc.fr/item/SB_1991-1992__34__345_0/
LA  - en
ID  - SB_1991-1992__34__345_0
ER  - 
%0 Book Section
%A Barlow, Martin
%T Harmonic analysis on fractal spaces
%B Séminaire Bourbaki : volume 1991/92, exposés 745-759
%A Collectif
%S Astérisque
%Z talk:755
%D 1992
%P 345-368
%N 206
%I Société mathématique de France
%U http://geodesic.mathdoc.fr/item/SB_1991-1992__34__345_0/
%G en
%F 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. | Zbl | MR

[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. | Zbl | MR | Numdam

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

[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. | Zbl | MR

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

[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. | Zbl | MR | Numdam

[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. | Zbl | MR

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

[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. | Zbl | MR

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

[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. | Zbl | MR

[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. | Zbl | MR

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

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

[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 | Zbl | MR

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

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

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

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

[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. | Zbl | MR

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