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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Gradients of Laplacian eigenfunctions on the Sierpinski gasket
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by Jessica L. DeGrado, Luke G. Rogers and Robert S. Strichartz PDF
Proc. Amer. Math. Soc. 137 (2009), 531-540 Request permission

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
  • MR Author ID: 785199
  • Email: rogers@math.uconn.edu
  • Robert S. Strichartz
  • Affiliation: Department of Mathematics, Cornell University, Ithaca, New York 14853-4201
  • Email: str@math.cornell.edu
  • 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
  • © Copyright 2008 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 137 (2009), 531-540
  • MSC (2000): Primary 28A80; Secondary 33E30
  • DOI: https://doi.org/10.1090/S0002-9939-08-09711-6
  • MathSciNet review: 2448573