Abstract. We study the operators of differentiation and of integration and the Hardy operator on weighted Banach spaces of entire functions. We estimate the norm of the operators, study the spectrum, and analyze when they are surjective, power bounded, hypercyclic and (uniformly) mean ergodic.

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In this paper, we merge two theories: that of pulse processes on weighted digraphs and that of evolution algebras. We enrich both of them. In fact, we obtain new results in the theory of pulse processes thanks to the new algebraic tool that we introduce in its framework, also extending the theory of evolution algebras, as well as its applications.

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