Harmonic analysis for resistance forms

Journal of Functional Analysis

Volumn 204, Issue 2, 2003, Pages 399-444

  Kigami, Jun ^a  

^a KYOTO UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0344118760     PISSN: 00221236     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0022-1236(02)00149-0     Document Type: Article

References (23)

1. M.T. Barlow, Diffusion on Fractals, in: Lecture Notes in Mathematics, Vol. 1690, Springer, Berlin, 1998.
2. M.T. Barlow, R.F. Bass, The construction of Brownian motion on the Sierpinski carpet, Ann. Inst. Henri Poincaré 25 (1989) 225-257.
3. M.T. Barlow, R.F. Bass, Local time for Brownian motion on the Sierpinski carpet, Probab. Theory Related Fields 85 (1990) 91-104.
4. M.T. Barlow, R.F. Bass, On the resistance of the Sierpinski carpet, Proc. Roy. Soc. London A 431 (1990) 354-360.
5. M.T. Barlow, R.F. Bass, Transition densities for Brownian motion on the Sierpinski carpet, Probab. Theory Related Fields 91 (1992) 307-330.
6. M.T. Barlow, E.A. Perkins, Brownian motion on the Sierpinski gasket, Probab. Theory Related Fields 79 (1988) 542-624.
7. A.K. Chandra, P. Raghavan, W.L. Ruzzo, R. Smolensky, P. Twari, The electrical resistance of a graph captures its commute and cover times, Proceedings of the 21st ACM Symposium on Theory of Computing, 1989.
8. P.J. Fitzsimmons, B.M. Hambly, T. Kumagai, Transition density estimates for Brownian motion on affine nested fractals, Comm. Math. Phys. 165 (1994) 595-620.
9. M. Fukushima, Y. Oshima, M. Takeda, Dirichlet Forms and Symmetric Markov Processes, de Gruyter Studies in Mathematics, Vol. 19, de Gruyter, Berlin, 1994.
10. B.M. Hambly, Brownian motion on a homogeneous random fractal, Probab. Theory Related Fields 94 (1992) 1-38.
11. B.M. Hambly, Brownian motion on a random recursive Sierpinski gasket, Ann. Probab. 25 (1997) 1059-1102.
12. B.M. Hambly, Heat kernels and spectral asymptotics for some random Sierpinski gaskets, in: C. Bandt, et al., (Eds.), Fractal Geometry and Stochastics II, Progress in Probability, Vol. 46, Birkhäuser, Berlin, 2000, pp. 239-267.
13. B.M. Hambly, T. Kumagai, Transition density estimates for diffusion processes on post critically finite self-similar fractals, Proc. London Math. Soc. 78 (3) (1999) 431-458.
14. B.M. Hambly, S.O.G. Nyberg, Finitely ramified graph directed fractals, spectral asymptotics and the multidimensional renewal theorem, preprint.
15. J. Kigami, Effective resistances for harmonic structures on p.c.f. self-similar sets, Math. Proc. Cambridge Philos. Soc. 115 (1994) 291-303.
16. J. Kigami, Analysis on Fractals, Cambridge Tracts in Mathematics, Vol. 143, Cambridge University Press, Cambridge, 2001.
17. J. Kigami, R.S. Strichartz, K.C. Walker, Constructing a Laplacian on the diamond fractal, Experimental Math. 10 (2001) 437-448.
18. T. Kumagai, Estimates of the transition densities for Brownian motion on nested fractals, Probab. Theory Related Fields 96 (1993) 205-224.
19. S. Kusuoka, X.Y. Zhou, Dirichlet forms on fractals: Poincaré constant and resistance, Probab. Theory Related Fields 93 (1992) 169-196.
20. W. Rudin, Real and Complex Analysis, 3rd Edition, McGraw-Hill, New York, 1987.
21. R.S. Strichartz, Some properties of Laplacians on fractals, J. Funct. Anal. 164 (1999) 181-208.
22. R.S. Strichartz, M. Usher, Splines on fractals, Math. Proc. Cambridge Philos. Soc. 129 (2000) 331-360.
23. T. Watanabe, Analysis on self-similar sets with general boundaries, in Japanese, Master Thesis, Kyoto University, 2002.