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arXiv · 2606.10943

$\rho$-Frequently Hypercyclic Operators

Tom Carroll·Clifford Gilmore
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Abstract

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.

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Tom Carroll, Clifford Gilmore. 2026-06-09. $\rho$-Frequently Hypercyclic Operators. https://arxiv.org/abs/2606.10943

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