The aim of this paper is to introduce some new concepts that provide the space of tempered distributions with certain "linear" structures in addition to its natural structure of linear vector space. These new concepts give for the rst time a precise mathematical meaning to the concepts of linear superposition used in physicsand in particular in quantum mechanics. The new concepts are: 1) S-family of tempered distributions; 2) operator generated by an S-family of tempered distributions; 3) families of class SL; 4) ultralinear combinations of a family of class SL; 5) superposition of an SL-family with respect to a family of distributions.
Principles of a generalization of the linear algebra in the spaces of tempered distributions
CARFI', David
1997-01-01
Abstract
The aim of this paper is to introduce some new concepts that provide the space of tempered distributions with certain "linear" structures in addition to its natural structure of linear vector space. These new concepts give for the rst time a precise mathematical meaning to the concepts of linear superposition used in physicsand in particular in quantum mechanics. The new concepts are: 1) S-family of tempered distributions; 2) operator generated by an S-family of tempered distributions; 3) families of class SL; 4) ultralinear combinations of a family of class SL; 5) superposition of an SL-family with respect to a family of distributions.Pubblicazioni consigliate
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
