Exact spectral asymptotics on the Sierpinski gasket
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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.References
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Additional Information
- Robert S. Strichartz
- Affiliation: Department of Mathematics, Cornell University, Ithaca, New York 14853
- Email: str@math.cornell.edu
- 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
- © Copyright 2011
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 140 (2012), 1749-1755
- MSC (2010): Primary 28A80
- DOI: https://doi.org/10.1090/S0002-9939-2011-11309-1
- MathSciNet review: 2869159