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Range of the horocyclic Radon transform on trees

Enrico Casadio TarabusiJoel M. CohenFlavia Colonna — 2000

Annales de l'institut Fourier

In this paper we study the Radon transform R on the set of horocycles of a homogeneous tree T , and describe its image on various function spaces. We show that the functions of compact support on that satisfy two explicit constitute the image under R of functions of finite support on T . We extend these results to spaces of functions with suitable decay on T , whose image under R satisfies corresponding decay conditions and contains distributions on that are not defined pointwise. We also show...

Radial Heat Diffusion from the Root of a Homogeneous Tree and the Combinatorics of Paths

Joel M. CohenMauro PagliacciMassimo A. Picardello — 2008

Bollettino dell'Unione Matematica Italiana

We compute recursively the heat semigroup in a rooted homogeneous tree for the diffusion with radial (with respect to the root) but non-isotropic transition probabilities. This is the discrete analogue of the heat operator on the disc given by Δ + c r for some constant c that represents a drift towards (or away from) the origin.

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