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A Moiré pattern on symmetric spaces of the noncompact type

Author: Alexandre Afgoustidis
Journal: Proc. Amer. Math. Soc. 146 (2018), 3747-3758
MSC (2010): Primary 43A85, 53C35; Secondary 43A90, 22E46
Published electronically: May 15, 2018
MathSciNet review: 3825830
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Abstract: We prove that if $X$ is a symmetric space of the noncompact type, just as adding Helgason waves which propagate in all directions will yield an elementary spherical function for $X$, a Helgason wave can be produced by adding elementary spherical functions whose centers describe a horocycle in $X$.

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Additional Information

Alexandre Afgoustidis
Affiliation: CEREMADE, Université Paris-Dauphine, PSL, Place du Maréchal de Lattre de Tas- signy, 75775 Paris Cedex 16, France
MR Author ID: 1121480

Keywords: Spherical functions, Riemannian symmetric spaces, Fourier-Helgason transform, neuroscience.
Received by editor(s): July 16, 2016
Published electronically: May 15, 2018
Additional Notes: The research in this paper was conducted while the author was a Ph.D. student at Université Paris 7 and IMJ-PRG (Institut de Mathématiques de Jussieu-Paris Rive Gauche).
Communicated by: Mourad E.H. Ismail
Article copyright: © Copyright 2018 American Mathematical Society