Normal Extensions of Differential Operators for Degenerate First-order

In this paper, it is investigated that necessary and sufficient conditions for a minimal operator defined by a degenerate first-order differential operator expression in the Hilbert space \(L_{2}(H,(a,b)),\,a,b\in\mathbb{R}\) to be formally normal. Also, all normal extensions of the minimal operator are given with their domains. Moreover, the spectrum set of these normal extensions is given through the family of evolution operators.