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arXiv · 1110.5816

Exact Spectral Asymptotics on the Sierpinski Gasket

Robert S. Strichartz
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Abstract

One of the ways that analysis on fractals is more complicated than analysis on manifolds is that the asymptotic behavior of the spectral counting function $N(t)$ has a power law modulated by a nonconstant multiplicatively periodic function. Nevertheless, we show that for the Sierpinski gasket it is possible to write an exact formula, with no remainder term, valid for almost every $t$. This is a stronger result than is valid on manifolds.

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Robert S. Strichartz. 2011-10-26. Exact Spectral Asymptotics on the Sierpinski Gasket. https://arxiv.org/abs/1110.5816

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