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