Axiomatic Construction of Trees from Boundary Arcs

Author:

Casadio Tarabusi EnricoORCID,Picardello Massimo A.

Abstract

AbstractThe aim of this article is to identify a set of independent axioms that characterize the end-point boundary $$\Omega $$ Ω of a tree T and to develop a procedure to (re)construct T and its geometric features from $$\Omega $$ Ω .

Funder

Università degli Studi di Roma La Sapienza

Publisher

Springer Science and Business Media LLC

Subject

General Mathematics

Reference10 articles.

1. Cartier, P.: Fonctions harmoniques sur un arbre, Calcolo delle probabilità (INdAM, Rome, 1971): Sympos. Math., vol IX, pp. 203–270. Academic Press, London (1972)

2. Cartier, P.: Géométrie et analyse sur les arbres. Exp. No. 407, Séminaire Bourbaki, 24ème année (1971/1972), Lecture Notes in Math., vol. 317, pp. 123–140. Springer, Berlin (1973)

3. Casadio Tarabusi, E., Gindikin, S. G., Picardello, M. A.: Integral geometry and harmonic analysis on homogeneous trees (2022) to appear. arXiv:math2002.09099

4. Casadio Tarabusi, E., Picardello, M.A.: Radon transforms in hyperbolic spaces and their discrete counterparts. Complex Anal. Oper. Theory 15(1), 40 (2021). https://doi.org/10.1007/s11785-020-01055-6. (paper no. 13)

5. Davidoff, G.P., Sarnak, P.C., Valette, A.: Elementary number theory, group theory, and Ramanujan graphs, London Math. Soc. Stud. Texts, vol. 55. Cambridge University Press, Cambridge (2003)

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