publication . Preprint . 2012

Spectral Analysis and Dirichlet Forms on Barlow-Evans Fractals

Steinhurst, Benjamin; Teplyaev, Alexander;
Open Access English
  • Published: 23 Apr 2012
Comment: v3: major revision
free text keywords: Mathematics - Classical Analysis and ODEs, Mathematics - Spectral Theory, 81Q35, 28A80, 31C25, 34L10, 47A10, 60J35, 81Q12
Related Organizations
Funded by
NSF| Random, Stochastic, and Self-similar Equations
  • Funder: National Science Foundation (NSF)
  • Project Code: 0505622
  • Funding stream: Directorate for Mathematical & Physical Sciences | Division of Mathematical Sciences
Download from
26 references, page 1 of 2

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

[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.

[11] (MR1133391) N. Bouleau and F. Hirsch, “Dirichlet forms and analysis on Wiener space,” de Gruyter Studies in Mathematics vol 14. Walter de Gruyter & Co., Berlin, 1991.

[12] (MR1303354) M. Fukushima, Y. O¯ shima, and M. Takeda, Dirichlet forms and symmetric Markov processes, volume 19 of de Gruyter Studies in Mathematics, Walter de Gruyter & Co., Berlin, 1994.

[13] (MR743439) A. Grigor'yan, Heat kernels on metric measure spaces with regular volume growth, In “Handbook of geometric analysis,” Adv. Lect. Math. (ALM) 13, 1-60. Int. Press, Somerville, MA, 2010.

[14] (MR1016814) J. G. Hocking and G. S. Young. “Topology,” 2nd edition, Dover Publications Inc., New York, 1988.

[15] C. Kaufmann, R. Kesler, A. Parshall, E. Stamey, B. Steinhurst, Quantum mechanics on Laakso spaces, J. Math. Phys., 53 (2012) 042102.

26 references, page 1 of 2
Powered by OpenAIRE Open Research Graph
Any information missing or wrong?Report an Issue