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.
S'operators and generated families
GERMANA', CLARA;CARFI', David
2000-01-01
Abstract
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.Pubblicazioni consigliate
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