rho-Frequently Hypercyclic Operators

The concept of $\rho$-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 $\rho$. A $\rho$-Frequent Hypercyclicity Criterion is determined and the $\rho$-frequent hypercyclicity of weighted backward shifts is investigated.