Spectral Analysis and Dirichlet Forms on Barlow-Evans Fractals

Preprint English OPEN
Steinhurst, Benjamin; Teplyaev, Alexander;
  • Subject: 81Q35, 28A80, 31C25, 34L10, 47A10, 60J35, 81Q12 | Mathematics - Classical Analysis and ODEs | Mathematics - Spectral Theory

We develop the foundation of the spectral analysis on Barlow-Evans projective limit fractals, or vermiculated spaces, which corresponds to symmetric Markov processes on these spaces. For some new examples, such as the generalized Laakso spaces and a Spierpinski P\^ate \... View more
  • References (26)
    26 references, page 1 of 3

    [1] E. Akkermans, G. Dunne, A. Teplyaev Physical consequences of complex dimensions of fractals, Europhys. Lett. 88 (2009) 40007.

    [2] (MR2450694) N. Bajorin, T. Chen, A. Dagan, C. Emmons, M. Hussein, M. Khalil, P. Mody, B. Steinhurst and A. Teplyaev, Vibration modes of 3n-gaskets and other fractals, J. Phys. A: Math Theor. 41 (2008) 015101.

    [3] (MR2451619) N. Bajorin, T. Chen, A. Dagan, C. Emmons, M. Hussein, M. Khalil, P. Mody, B. Steinhurst, A. Teplyaev, Vibration spectra of finitely ramified, symmetric fractals, Fractals 16 (2008) 243-258.

    [4] (MR1668115) M. T. Barlow, Diffusions on fractals, Lectures on Probability Theory and Statistics (SaintFlour, 1995), 1-121, Lecture Notes in Math., 1690, Springer, Berlin, 1998.

    [5] (MR2039950) M. T. Barlow, Heat kernels and sets with fractal structure. Contemp. Math. 338, (2003).

    [6] (MR2076770) M. T. Barlow, Which values of the volume growth and escape time exponent are possible for a graph? Revista Math. Iberoamericana. 20, (2004), 1-31.

    [7] (MR1701339) M. T. Barlow and R. F. Bass. Brownian motion and harmonic analysis on Sierpinski carpets, Canad. J. Math., 51:4 (1999), 673-744.

    [8] (MR2639316) M. T. Barlow, R. F. Bass, T. Kumagai, and A. Teplyaev, Uniqueness of Brownian motion on Sierpin´ski carpets. J. Eur. Math. Soc. (JEMS), 12(3):655-701, 2010.

    [9] (MR1833895) M. T. Barlow, T. Coulhon and A. Grigor'yan, Manifolds and graphs with slow heat kernel decay. Invent. Math. 144 (2001), no. 3, 609-649.

    [10] (MR2087787) M. T. Barlow and S. N. Evans, Markov processes on vermiculated spaces, In “Random walks and geometry,” Walter de Gruyter GmbH & Co. KG, Berlin, (2004), 337-348.

  • Related Organizations (1)
  • Metrics
Share - Bookmark