Convergence and uniqueness problems for Dirichlet forms on fractals

Roberto Peirone

Bollettino dell'Unione Matematica Italiana (2000)

  • Volume: 3-B, Issue: 2, page 431-460
  • ISSN: 0392-4041

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Peirone, Roberto. "Convergence and uniqueness problems for Dirichlet forms on fractals." Bollettino dell'Unione Matematica Italiana 3-B.2 (2000): 431-460. <http://eudml.org/doc/195578>.

@article{Peirone2000,
author = {Peirone, Roberto},
journal = {Bollettino dell'Unione Matematica Italiana},
keywords = {self-similar fractals; homogenization; Dirichlet integral; Dirichlet form; renormalization map; weak ergodicity; strong ergodicity},
language = {eng},
month = {6},
number = {2},
pages = {431-460},
publisher = {Unione Matematica Italiana},
title = {Convergence and uniqueness problems for Dirichlet forms on fractals},
url = {http://eudml.org/doc/195578},
volume = {3-B},
year = {2000},
}

TY - JOUR
AU - Peirone, Roberto
TI - Convergence and uniqueness problems for Dirichlet forms on fractals
JO - Bollettino dell'Unione Matematica Italiana
DA - 2000/6//
PB - Unione Matematica Italiana
VL - 3-B
IS - 2
SP - 431
EP - 460
LA - eng
KW - self-similar fractals; homogenization; Dirichlet integral; Dirichlet form; renormalization map; weak ergodicity; strong ergodicity
UR - http://eudml.org/doc/195578
ER -

References

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  1. BARLOW, M. T., Random Walks, Electrical Resistance, and Nested Fractals, in Asymptotic Problems in Probability Theory: Stochastic Models and Diffusion on Fractals, pp. 131-157. Pitman Research Notes in Math. Series, n. 283, 1993. Zbl0791.60097MR1354153
  2. FITZSIMMONS, P. J.- HAMBLY, B. M.- KUMAGAI, T., Transition Density Estimates for Brownian Motion on Affine Nested Fractals, Comm. Math. Phys., 165 (1994), 595-620. Zbl0853.60062MR1301625
  3. FUKUSHIMA, M.- OSHIMA, Y.- TAKEDA, M., Dirichlet Forms and Symmetric Markov Processes, de Gruyter Stud. Math.19, Walter de Gruyter, Berlin-New York1994. Zbl0838.31001MR1303354
  4. HATTORI, K.- HATTORI, T.- WATANABE, H., Gaussian Field Theories on General Networks and the Spectral Dimension, Progr. Theor. Phys. Suppl., 92 (1987), 108-143. MR934668
  5. HUTCHINSON, J. E., Fractals and Self Similarity, Ind. Univ. Math. Journ., 30 (1981), 713-747. Zbl0598.28011MR625600
  6. KIGAMI, J., Harmonic Calculus on p.c.f. Self-similar Sets, Trans. Amer. Math. Soc., 335 (1993), 721-755. Zbl0773.31009MR1076617
  7. KIGAMI, J., Harmonic Metric and Dirichlet Form on the Sierpinski Gasket, in Asymptotic Problems in Probability Theory: Stochastic Models and Diffusion on Fractals, pp. 201-218, Pitman Research Notes in Math. Series, n. 283, 1993. Zbl0793.31005MR1354156
  8. KOZLOV, S. M., Harmonization and Homogenization on Fractals, Comm. Math. Phys., 153 (1993), 339-357. Zbl0767.58033MR1218305
  9. KUMAGAI, T.- KUSUOKA, S., Homogenization on Nested Fractals, Probab. Theory Related Fields, 104 (1996), 375-398. Zbl0843.31004MR1376343
  10. LINDSTRØM, T., Brownian Motion on Nested Fractals, Mem. Amer. Math. Soc. No. 420 (1990). Zbl0688.60065MR988082
  11. METZ, V., How many Diffusions Exist on the Vicsek Snowflake?, Acta Appl. Math., 32 (1993), 227-241. Zbl0795.31011MR1255630
  12. METZ, V., Renormalization of Finitely Ramified Fractals, Proc. Roy. Soc. Edinburgh, 125A (1995), 1085-1104. Zbl0874.28010MR1361635
  13. METZ, V., Hilbert's Projective Metric on Cones of Dirichlet Forms, Journal of Functional Analysis, 127 (1995), 438-455. Zbl0831.47047MR1317725
  14. METZ, V., Renormalization Contracts on Nested Fractals, J. Reine Angew. Math., 480 (1996), 161-175. Zbl0858.31008MR1420562
  15. MORTOLA, S.- PEIRONE, R., Homogenization of Quadratic Forms on Fractals, Rendiconti del Seminario Matematico e Fisico di Milano, LXIV (1994), 117-128. Zbl0853.58078MR1397467
  16. NUSSBAUM, R. D., Hilbert's Projective Metric and Iterated Nonlinear Maps, Mem. Amer. Math. Soc. No 391 (1988). Zbl0666.47028MR961211
  17. SABOT, C., Diffusions sur les Espaces Fractals, Thèse de Doctorat, Université Paris 6, Paris (1995). 
  18. SENETA, E., Non-negative Matrices and Markov Chains, Springer-Verlag, New York, 1981. Zbl0471.60001MR2209438

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