Exact spectral asymptotics on the Sierpinski gasket
Author:
Robert S. Strichartz
Journal:
Proc. Amer. Math. Soc. 140 (2012), 1749-1755
MSC (2010):
Primary 28A80
Posted:
September 22, 2011
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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
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
DOI:
http://dx.doi.org/10.1090/S0002-9939-2011-11309-1
PII:
S 0002-9939(2011)11309-1
Keywords:
Sierpinski gasket,
Laplacians on fractals,
spectral asymptotics
Received by editor(s):
January 28, 2011
Posted:
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
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 
. This is a stronger result than is valid on manifolds. 