Restrictions of harmonic functions and Dirichlet eigenfunctions of the Hata set to the interval

References

[1] Adams B., Smith S. A., Strichartz R. S. and Teplyaev A., The spectrum of the Laplacian on the pentagasket, Fractals in Graz 2001, Trends Math., Birkhäuser, Basel (2003), 1–24. 10.1007/978-3-0348-8014-5_1Search in Google Scholar

[2] Constantin S., Strichartz R. S. and Wheeler M., Analysis of the Laplacian and spectral operators on the Vicsek set, Commun. Pure Appl. Anal. 10 (2011), no. 1, 1–44. 10.3934/cpaa.2011.10.1Search in Google Scholar

[3] Dalrymple K., Strichartz R. S. and Vinson J. P., Fractal differential equations on the Sierpinski gasket, J. Fourier Anal. Appl. 5 (1999), 203–284. 10.1007/BF01261610Search in Google Scholar

[4] de Amo E., Díaz Carrillo M. and Fernández Sánchez J., Harmonic analysis on the Sierpiński gasket and singular functions, Acta Math. Hungar. 143 (2014), no. 1, 58–74. 10.1007/s10474-013-0373-1Search in Google Scholar

[5] Demir B., Dzhafarov V., Koçak Ş. and Üreyen M., Derivatives of the restrictions of harmonic functions on the Sierpinski gasket to segments, J. Math. Anal. Appl. 333 (2007), no. 2, 817–822. 10.1016/j.jmaa.2006.11.025Search in Google Scholar

[6] Hata M., On the structure of self-similar sets, Japan J. Appl. Math. 2 (1985), no. 2, 381–414. 10.1007/BF03167083Search in Google Scholar

[7] Hutchinson J. E., Fractals and self-similarity, Indiana Univ. Math. J. 30 (1981), no. 5, 713–747. 10.1512/iumj.1981.30.30055Search in Google Scholar

[8] Kigami J., A harmonic calculus on the Sierpiński spaces, Japan J. Appl. Math. 6 (1989), no. 2, 259–290. 10.1007/BF03167882Search in Google Scholar

[9] Kigami J., Harmonic calculus on p.c.f. self-similar sets, Trans. Amer. Math. Soc. 335 (1993), no. 2, 721–755. Search in Google Scholar

[10] Kigami J., Effective resistances for harmonic structures on p.c.f. self-similar sets, Math. Proc. Cambridge Philos. Soc. 115 (1994), no. 2, 291–303. 10.1017/S0305004100072091Search in Google Scholar

[11] Kigami J., Analysis on Fractals, Cambridge University Press, Cambridge, 2001. 10.1017/CBO9780511470943Search in Google Scholar

[12] Sáenz R. A., Nontangential limits and Fatou-type theorems on post-critically finite self-similar sets, J. Fourier Anal. Appl. 18 (2012), no. 2, 240–265. 10.1007/s00041-011-9194-1Search in Google Scholar

[13] Shima T., On eigenvalue problems for the random walks on the Sierpiński pre-gaskets, Japan J. Indust. Appl. Math. 8 (1991), no. 1, 127–141. 10.1007/BF03167188Search in Google Scholar

[14] Strichartz R. S., Differential Equations on Fractals, Princeton University Press, Princeton, 2006. 10.1515/9780691186832Search in Google Scholar

[15] Yamaguti M., Hata M. and Kigami J., Mathematics of Fractals, American Mathematical Society, Providence, 1997; translated from the 1993 Japanese original by Kiki Hudson. 10.1090/mmono/167Search in Google Scholar