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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 756075, 8 pages
Explicit Spectral Decimation for a Class of Self-Similar Fractals
Centro de Investigación en Matemáticas, Universidad Autónoma del Estado de Hidalgo, 42184 Pachuca, HGO, Mexico
Received 6 September 2012; Revised 22 December 2012; Accepted 3 January 2013
Academic Editor: Jiaxin Hu
Copyright © 2013 Sergio A. Hernández and Federico Menéndez-Conde. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- J. Kigami, “A harmonic calculus on the Sierpiński spaces,” Japan Journal of Applied Mathematics, vol. 6, no. 2, pp. 259–290, 1989.
- J. Kigami, “Harmonic calculus on p.c.f. self-similar sets,” Transactions of the American Mathematical Society, vol. 335, no. 2, pp. 721–755, 1993.
- M. Fukushima and T. Shima, “On a spectral analysis for the Sierpiński gasket,” Potential Analysis, vol. 1, no. 1, pp. 1–35, 1992.
- T. Shima, “On eigenvalue problems for Laplacians on p.c.f. self-similar sets,” Japan Journal of Industrial and Applied Mathematics, vol. 13, no. 1, pp. 1–23, 1996.
- T. Lindstrøm, “Brownian motion on nested fractals,” Memoirs of the American Mathematical Society, no. 420, 1990.
- S. Constantin, R. S. Strichartz, and M. Wheeler, “Analysis of the Laplacian and spectral operators on the Vicsek set,” Communications on Pure and Applied Analysis, vol. 10, no. 1, pp. 1–44, 2011.
- S. Drenning and R. S. Strichartz, “Spectral decimation on Hambly's homogeneous hierarchical gaskets,” Illinois Journal of Mathematics, vol. 53, no. 3, pp. 915–937, 2010.
- D. J. Ford and B. Steinhurst, “Vibration spectra of the -tree fractal,” Fractals, vol. 18, no. 2, pp. 157–169, 2010.
- V. Metz, “‘Laplacians’ on finitely ramified, graph directed fractals,” Mathematische Annalen, vol. 330, no. 4, pp. 809–828, 2004.
- D. Zhou, “Spectral analysis of Laplacians on the Vicsek set,” Pacific Journal of Mathematics, vol. 241, no. 2, pp. 369–398, 2009.
- N. Bajorin, T. Chen, A. Dagan et al., “Vibration modes of -gaskets and other fractals,” Journal of Physics A, vol. 41, no. 1, Article ID 015101, 21 pages, 2008.
- N. Bajorin, T. Chen, A. Dagan et al., “Vibration spectra of finitely ramified, symmetric fractals,” Fractals, vol. 16, no. 3, pp. 243–258, 2008.
- R. S. Strichartz, “Fractafolds based on the Sierpiński gasket and their spectra,” Transactions of the American Mathematical Society, vol. 355, no. 10, pp. 4019–4043, 2003.
- K. E. Hare and D. Zhou, “Gaps in the ratios of the spectra of Laplacians on fractals,” Fractals, vol. 17, no. 4, pp. 523–535, 2009.
- R. S. Strichartz, “Laplacians on fractals with spectral gaps have nicer Fourier series,” Mathematical Research Letters, vol. 12, no. 2-3, pp. 269–274, 2005.
- D. Zhou, “Criteria for spectral gaps of Laplacians on fractals,” The Journal of Fourier Analysis and Applications, vol. 16, no. 1, pp. 76–96, 2010.
- R. S. Strichartz, Differential Equations on Fractals: A Tutorial, Princeton University Press, Princeton, NJ, USA, 2006.
- J. Kigami, Analysis on Fractals, vol. 143, Cambridge University Press, Cambridge, UK, 2001.