Abstract
We analyze f-frequently hypercyclic, q-frequently hypercyclic ( $$q> 1$$ ), and frequently hypercyclic $$C_{0}$$ -semigroups ( $$q=1$$ ) defined on complex sectors,with values in separable infinite-dimensional Fréchet spaces. Some structural results are given for a general class of $${\mathcal F}$$ -frequently hypercyclic $$C_{0}$$ -semigroups, as well. We investigate generalized frequently hypercyclic translation semigroups and generalized frequently hypercyclic semigroups induced by semiflows on weighted function spaces. Several illustrative examples are presented.
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