Characterization of the range of the Radon transform on homogeneous trees.
Converse mean value theorems on trees and symmetric spaces.
Coherent Graded Rings and the Non-Existence of Spaces of Finite Stable Homotopy Type.
Range of the horocyclic Radon transform on trees
In this paper we study the Radon transform on the set of horocycles of a homogeneous tree , 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 of functions of finite support on . We extend these results to spaces of functions with suitable decay on , whose image under 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
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 for some constant that represents a drift towards (or away from) the origin.
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