Abstract.
Let ? be a homogeneous tree, ℒbe the Laplace operator of ?, and b be the bottom of its L 2 spectrum. Let u be a solution of the (modified) wave equation on ?. Using Fourier analysis on ? we show that the energy of u is asymptotically divided into equal potential and kinetic parts.
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Received 13 January 1997; in final form 23 March 1998
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Medolla, G. Asymptotic Energy Equipartition for the Wave Equation on Homogeneous Trees. Mh Math 127, 43–53 (1999). https://doi.org/10.1007/s006050050021
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DOI: https://doi.org/10.1007/s006050050021