Estimates of the local spectral dimension of the Sierpinski gasket
Masanori Hino
TL;DR
This paper provides quantitative estimates of the local spectral dimension of the two-dimensional Sierpinski gasket, building on previous work related to energy measures and harmonic functions on fractals.
Contribution
It introduces new quantitative methods for estimating the local spectral dimension of the Sierpinski gasket, inspired by prior studies of energy measures.
Findings
Quantitative estimates of the local spectral dimension obtained.
Connections established between spectral dimension and energy measures.
Methodology applicable to other fractal structures.
Abstract
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 Sierpi\'nski gasket, Indiana Univ. Math. J. 63 (2014), 831-868].
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Taxonomy
TopicsMathematical Dynamics and Fractals · Analytic Number Theory Research · advanced mathematical theories