The dynamics of the left translation semigroup {Tt}t≥0 on weighted Lp spaces over a directed metric tree L(G) is investigated. Necessary and sufficient conditions on the weight family ρ for the strong continuity of the semigroup are provided. Furthermore, hypercyclicity and weak mixing properties are characterized in terms of the asymptotic decay of ρ along the tree structure. These results generalize classical Lp translation semigroup dynamics to a graph setting.
Dynamics of the translation semigroup on directed metric trees
Mangino, Elisabetta
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2026-01-01
Abstract
The dynamics of the left translation semigroup {Tt}t≥0 on weighted Lp spaces over a directed metric tree L(G) is investigated. Necessary and sufficient conditions on the weight family ρ for the strong continuity of the semigroup are provided. Furthermore, hypercyclicity and weak mixing properties are characterized in terms of the asymptotic decay of ρ along the tree structure. These results generalize classical Lp translation semigroup dynamics to a graph setting.File in questo prodotto:
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