Let X be a symmetric graph of type k and order r, where k,r ≥ 2 are integers. In this paper we give explicite expressions of the horocyclic Abel transform and its dual, as well as their inverses X. We then derive the Plancherel measure for the Helgason-Fourier transform on G and give a version of the Kunze-Stein phenomenon thereon. Finally, we compute the solution to the shifted wave equation on X, using Àsgeirsson's mean value theorem and the inverse dual Abel transform.
Publié le : 2015-05-27
Classification:
Symmetric graph,
Horocycles,
Abel transform,
dual Abel transform,
Spherical Fourier transformation,
Spherical Fourier transform.,
Wave equation,
44A12, 43A90, 39A12,
[MATH.MATH-GR]Mathematics [math]/Group Theory [math.GR],
[INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering
@article{hal-00961721,
author = {Jamal Eddine, Alaa},
title = {An overview of harmonic analysis and the shifted wave equation on symmetric graphs},
journal = {HAL},
volume = {2015},
number = {0},
year = {2015},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-00961721}
}
Jamal Eddine, Alaa. An overview of harmonic analysis and the shifted wave equation on symmetric graphs. HAL, Tome 2015 (2015) no. 0, . http://gdmltest.u-ga.fr/item/hal-00961721/