Dirac-orthogonality in the space of tempered distributions (Q1874146)

The main goal of this paper, in the author's opinion, is to present a mathematical basis to a formalism of quantum mechanics. He starts with the space of tempered distributions, defines a regular tempered distribution by \(f\in O_M\), \(S\)-family and regular family of tempered distributions, giving some properties of them. It would be interesting to compare these results with those on distributional valued functions. In this way it is possible to define ``quantum extension of a regular operator'' and ``\(\delta\)-orthogonality'' and ``\(\delta\)-orthonormality''.