$\ddot{I}$-Frequently Hypercyclic Operators

Abstract

The concept of $\ddot{I}$-frequent hypercyclicity is introduced in order to provide a refined form of frequent hypercyclicity. This is achieved by replacing the denominator in the definition of frequent hypercyclicity by an appropriately chosen calibration function $\ddot{I}$. A $\ddot{I}$-Frequent Hypercyclicity Criterion is determined and the $\ddot{I}$-frequent hypercyclicity of weighted backward shifts is investigated.