Recurrence of Cosine Operator Functions on Groups
Printed: Dec 2016
In this note, we study the recurrence and topologically multiple
recurrence of a sequence of operators on Banach spaces.
In particular, we give a sufficient and necessary condition for
a cosine operator function,
induced by a sequence of operators on the Lebesgue space of a
locally compact group, to be topologically multiply recurrent.
topologically multiple recurrence, recurrence, topological transitivity, hypercyclicity, cosine operator function
47A16 - Cyclic vectors, hypercyclic and chaotic operators
54B20 - Hyperspaces
43A15 - $L^p$-spaces and other function spaces on groups, semigroups, etc.