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Gradients of Laplacian eigenfunctions on the Sierpinski gasket
Author(s):
Jessica
L.
DeGrado;
Luke
G.
Rogers;
Robert
S.
Strichartz
Journal:
Proc. Amer. Math. Soc.
137
(2009),
531-540.
MSC (2000):
Primary 28A80;
Secondary 33E30
Posted:
October 6, 2008
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Abstract:
We use spectral decimation to provide formulae for computing the harmonic tangents and gradients of Laplacian eigenfunctions on the Sierpinski Gasket. These formulae are given in terms of special functions that are defined as infinite products.
References:
-
- 1.
- M. Fukushima and T. Shima, On a spectral analysis for the Sierpiński gasket, Potential Anal. 1 (1992), no. 1, 1-35. MR 1245223 (95b:31009)
- 2.
- Marius Ionescu, Erin P. J. Pearse, Luke G. Rogers, Hou-Jun Ruan, and Robert S. Strichartz, The resolvent of the Laplacian on p.c.f. self-similar fractals, in preparation.
- 3.
- Jun Kigami, Analysis on fractals, Cambridge Tracts in Mathematics, vol. 143, Cambridge University Press, Cambridge, 2001. MR 1840042 (2002c:28015)
- 4.
- Leonid Malozemov and Alexander Teplyaev, Self-similarity, operators and dynamics, Math. Phys. Anal. Geom. 6 (2003), no. 3, 201-218. MR 1997913 (2004d:47012)
- 5.
- Jonathan Needleman, Robert S. Strichartz, Alexander Teplyaev, and Po-Lam Yung, Calculus on the Sierpinski gasket. I. Polynomials, exponentials and power series, J. Funct. Anal. 215 (2004), no. 2, 290-340. MR 2150975
- 6.
- Kasso A. Okoudjou, Luke G. Rogers, and Robert S. Strichartz, Generalized eigenfunctions and a Borel theorem on the Sierpinski gasket, Canad. Math. Bull., to appear; available at http://www.journals.cms.math.ca/cgi-bin/vault/viewprepub/okoudjou8913.prepub.
- 7.
- Robert S. Strichartz, Taylor approximations on Sierpinski gasket type fractals, J. Funct. Anal. 174 (2000), no. 1, 76-127. MR 1761364 (2001i:31018)
- 8.
- -, Differential equations on fractals, A tutorial, Princeton University Press, Princeton, NJ, 2006. MR 2246975 (2007f:35003)
- 9.
- Alexander Teplyaev, Gradients on fractals, J. Funct. Anal. 174 (2000), no. 1, 128-154. MR 1761365 (2001h:31012)
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Additional Information:
Jessica
L.
DeGrado
Affiliation:
Department of Mathematics, Cornell University, Ithaca, New York 14853-4201
Email:
jld69@cornell.edu
Luke
G.
Rogers
Affiliation:
Department of Mathematics, University of Connecticut, Storrs, Connecticut 06269-3009
Email:
rogers@math.uconn.edu
Robert
S.
Strichartz
Affiliation:
Department of Mathematics, Cornell University, Ithaca, New York 14853-4201
Email:
str@math.cornell.edu
DOI:
10.1090/S0002-9939-08-09711-6
PII:
S 0002-9939(08)09711-6
Received by editor(s):
November 14, 2007
Posted:
October 6, 2008
Additional Notes:
The research of the first author was supported by the National Science Foundation through the Research Experiences for Undergraduates (REU) Program at Cornell University.
The research of the third author was supported in part by the National Science Foundation, Grant DMS-0652440.
Communicated by:
Michael T. Lacey
Copyright of article:
Copyright
2008,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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