Sequences of differential operators: exponentials, hypercyclicity and equicontinuity
An eigenvalue criterion for hypercyclicity due to the first author is improved. As a consequence, some new sufficient conditions for a sequence of infinite order linear differential operators to be hypercyclic on the space of holomorphic functions on certain domains of $ℂ^N$ are shown. Moreover, several necessary conditions are furnished. The equicontinuity of a family of operators as above is also studied, and it is characterized if the domain is $ℂ^N$. The results obtained extend or improve earlier work of several authors.
- 47B38: Operators on function spaces (general)
- 30E10: Approximation in the complex domain
- 47A16: Cyclic vectors, hypercyclic and chaotic operators
- 47F05: Partial differential operators (should also be assigned at least one other classification number in section 47)
- 47E05: Ordinary differential operators (should also be assigned at least one other classification number in section 47)