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Exact spectral asymptotics on the Sierpinski gasket


Author: Robert S. Strichartz
Journal: Proc. Amer. Math. Soc. 140 (2012), 1749-1755
MSC (2010): Primary 28A80
Published electronically: September 22, 2011
MathSciNet review: 2869159
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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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Additional Information

Robert S. Strichartz
Affiliation: Department of Mathematics, Cornell University, Ithaca, New York 14853
Email: str@math.cornell.edu

DOI: https://doi.org/10.1090/S0002-9939-2011-11309-1
Keywords: Sierpinski gasket, Laplacians on fractals, spectral asymptotics
Received by editor(s): January 28, 2011
Published electronically: September 22, 2011
Additional Notes: Research supported in part by National Science Foundation grant DMS-0652440
Communicated by: Michael T. Lacey
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.