Dynamics of a C_۰-Semigroup of Translations on Locally Compact Groups

Let G be a locally compact group and ۱\le p<\infty. In this paper, we show that the mapping \pi: G\times L^p(G)\to L^p(G) with the assignment (t, f)\mapsto T_t f=\frac{\phi}{\delta_t*\phi}\delta_t*f, is separately continuous which ensures that \{T_t\}_{t\in G} forms a C_۰-semigroup. Also, it is proved that the C_۰-semigroup \{T_t\}_{t\in G} admits a universal vector only when G is noncompact and second countable. The hypercyclic phenomenon is studied for the single weighted translation as well. Finally, we give examples of universal C_۰-semigroups.

کلیدواژه ها:

translation ، Semigroup ، Locally compact ، Orbit ، Hypercyclic ، Universal