Hankel convolution operators on entire functions and distributions

Distributional chaos for backward shifts

“…i∈N 0 ,k∈N , and the linking isomorphism is g → (g (2i) (0)) i 0 (see [6,41] for more details). The series j∈N e 2 jk…”

Hypercyclic and chaotic convolution operators associated with the Dunkl operator on <Emphasis Type=?Bold?>C</Emphasis>

“…(i) ⇒ (ii). This assertion can be proved as Proposition 3.5 of [2] (see also the proof of Proposition 3.6 [3]). …”

“…is an eigenfunction of L associated with the eigenvalue Ψ(z). To see that L is hypercyclic and chaotic and that there exists a linear subspace M of H such that each nonzero element of M is hypercyclic for L, we can proceed as in [2,Proposition 3.6] (see also [3,Proposition 3.7]). …”

Untitled

“…This result was recently extended to Beurling and Romieu distributions by J. Bonet [15]. This question has been investigated by the authors in [5] on the space E of even distributions of compact support on IR. This question has been investigated by the authors in [5] on the space E of even distributions of compact support on IR.…”