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A decreasing rearrangement for functions on homogeneous trees

A decreasing rearrangement for functions on homogeneous trees
 
Garcia Domingo, Josep Lluís ; Soria, Javier
2005

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Enllaç permanent: http://hdl.handle.net/10854/2257
 
Versió de l'editor: https://doi.org/10.1016/j.ejc.2004.03.004
 

Abstract

We introduce a new decreasing rearrangement for functions defined on a homogeneous tree, which enjoys very intuitive and natural properties. The idea is to iterate, with respect to a particular ordering, the usual one dimensional rearrangement on each geodesic. After showing the canonicity of this definition and the axioms of ...»»»»
We introduce a new decreasing rearrangement for functions defined on a homogeneous tree, which enjoys very intuitive and natural properties. The idea is to iterate, with respect to a particular ordering, the usual one dimensional rearrangement on each geodesic. After showing the canonicity of this definition and the axioms of symmetrization, we prove our main result: the geometric and analytic definitions, in terms of the “layer cake” formula, agree.^^^^

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Article

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(c) 2005 Elsevier. Published article is available at: http://dx.doi.org/10.1016/j.ejc.2004.03.004

Citation:

Garcia Domingo, Josep Lluis, and J. Soria. "A Decreasing Rearrangement for Functions on Homogeneous Trees." European Journal of Combinatorics 26.2 (2005): 201-25.