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A continuous linear operator L defined on the space of entire functions H(C)is said to be an extended $lambda$-eigenoperator of the differentiationoperator D provided DL = $lambda$LD. Here we fully characterize when anextended $lambda$-eigenoperator of D is supercyclic, it has a hypercyclicsubspace or it has a supercyclic subspace.

Supercyclic properties of extended eigenoperators of the differentiation operator on the space of entire functions