Abstract
In this paper, the authors study some basic properties of the new generalized scalar product introduced recently by Carfı̀ in the space of tempered distributions. Such properties are the analogues of some basic properties fulfilled by the scalar product of a finite dimensional pre-Hilbertian space. The interest of this circumstance lies in the fact that the space of tempered distributions has not a pre-Hilbertian natural structure, moreover it is not a finite dimensional vector space.
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