Harmonic analysis on fractal spaces

Martin Barlow

Séminaire Bourbaki (1991-1992)

  • Volume: 34, page 345-368
  • ISSN: 0303-1179

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Barlow, Martin. "Harmonic analysis on fractal spaces." Séminaire Bourbaki 34 (1991-1992): 345-368. <http://eudml.org/doc/110158>.

@article{Barlow1991-1992,
author = {Barlow, Martin},
journal = {Séminaire Bourbaki},
keywords = {harmonic analysis; fractal space; heat equations},
language = {eng},
pages = {345-368},
publisher = {Société Mathématique de France},
title = {Harmonic analysis on fractal spaces},
url = {http://eudml.org/doc/110158},
volume = {34},
year = {1991-1992},
}

TY - JOUR
AU - Barlow, Martin
TI - Harmonic analysis on fractal spaces
JO - Séminaire Bourbaki
PY - 1991-1992
PB - Société Mathématique de France
VL - 34
SP - 345
EP - 368
LA - eng
KW - harmonic analysis; fractal space; heat equations
UR - http://eudml.org/doc/110158
ER -

References

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  7. [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. Zbl0905.60049
  8. [Ch] I. Chavel: Eigenvalues in Riemannian Geometry. Academic Press, 1984. Zbl0551.53001MR768584
  9. [F1] M. Fukushima: Dirichlet forms and Markov processes, North Holland1980. Zbl0422.31007MR569058
  10. [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. Zbl0764.60081MR1190496
  11. [FS] M. Fukushima and T. Shima: On a spectral analysis for the Sierpinski gasket. To appear J. of Potential Analysis. Zbl1081.31501MR1245223
  12. [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. Zbl0621.60073MR894545
  13. [HHW] K. Hattori, T. Hattori and H. Watanabe: Gaussian field theories and the spectral dimensions. Prog. Th. Phys. Supp. No. 92 (1987) 108-143. 
  14. [Kig1] J. Kigami: A harmonic calculus on the Sierpinski space. Japan J. Appl. Math.6 (1989) 259-290. Zbl0686.31003MR1001286
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  16. [Kum] T. Kumagai: Estimates of the transition densities for Brownian motion on nested fractals. Preprint 1991. MR1227032
  17. [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 Zbl0645.60081MR933827
  18. [K2] S. Kusuoka: Dirichlet forms on fractals and products of random matrices. Publ. RIMS Kyoto Univ., 25 (1989) 659-680. Zbl0694.60071MR1025071
  19. [KZ] S. Kusuoka and X.Y. Zhou: Dirichlet form on fractals: Poincaré constant and resistance. Probab. Th. Rel. Fields93, (1992) 169- 186. Zbl0767.60076MR1176724
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