Exact spectral asymptotics on the Sierpinski gasket

Strichartz, Robert

doi:10.1090/S0002-9939-2011-11309-1

Exact spectral asymptotics on the Sierpinski gasket
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Proc. Amer. Math. Soc. 140 (2012), 1749-1755 Request permission

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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