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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Gradients of Laplacian eigenfunctions on the Sierpinski gasket


Authors: Jessica L. DeGrado, Luke G. Rogers and Robert S. Strichartz
Journal: Proc. Amer. Math. Soc. 137 (2009), 531-540
MSC (2000): Primary 28A80; Secondary 33E30
Published electronically: October 6, 2008
MathSciNet review: 2448573
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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.


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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: http://dx.doi.org/10.1090/S0002-9939-08-09711-6
PII: S 0002-9939(08)09711-6
Received by editor(s): November 14, 2007
Published electronically: 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
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.