In this section, we are know about repeat and subspace-repeat of the C0- semigroups. Repetitive C0-semigroups and subspace-intermittent C0-semigroups are presented and their properties are examined. It is laid out that repetitive C0-semigroups and subspace-repetitive C0-semigroups can be constru-cted on nitedimensional Banach spaces. A few rules for recurrency are expressed in this section. Some of them depend on open sets, neighborhoods of nothing, and some of them depend on unique eigenvectors. Repetitive vectors are presented. It is demonstrated that in the event that a C0-semigroup has a thick arrangement of repetitive vectors, it is repetitive and it is demonstrated that a repetitive C0-semigroup has a thick arrangement of intermittent vectors. It is expressed that the repeat of the immediate amount of two C0-semigroups suggests that any of them is a repetitive C0-semigroup. The fact that the immediate total makes it shown of two blending C0-semigroups is intermittent. Likewise, if a C0-semigroup satises the Hypercyclicity Measure, it is repetitive.
Department of Mathematics, Farhangian University, Tehran, Iran.
Please see the link here: https://stm.bookpi.org/RHMCS-V1/article/view/8245
Keywords: Recurrent C0-semigroups, subspace-recurrent C0-semigroups, recurrence criteria, recurrent vectors, hyperc-yclic C0-semigroups, direct sum