The aim of this paper is to study some new concepts introduced by D.Carfì to generalize the linear structure of the space of tempered distri- butions. The new concepts are: 1) operator of class S0 or S0-operator; 2) family generated by an S0-operator; 3) superposition of a family of tempered distributions of class SL(see [Ca]) with respect to an operator; 4) image of a family of distributions under an operator A : S'n toS'm. These new concepts permit the development of a generalization of linear algebra in the space of tempered distributions and a more deeply study of some problems faced by linear algebra, as the theory of system, theory of decision, the optimal control, the quantum mechanics and so on.
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