Exact Spectral Asymptotics on the Sierpinski Gasket

Details Exact Spectral Asymptotics on the Sierpinski Gasket Exact Spectral Asymptotics on the Sierpinski Gasket

2011-10-26

arxiv.org/abs/1110.5816v1

Mathematics

Classical Analysis and ODEs

v1: 7 pages, 1 figure

Scientific paper

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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