Estimates of the local spectral dimension of the Sierpinski gasket

We discuss quantitative estimates of the local spectral dimension of the two-dimensional Sierpinski gasket. The present arguments were inspired by a previous study of the distribution of the Kusuoka measure by R. Bell, C.-W. Ho, and R. S. Strichartz [Energy measures of harmonic functions on the Sierpiński gasket, Indiana Univ. Math. J. 63 (2014), 831-868].