A class of first order degenerate di̇fferential operators and some their spectral problems

In this study, the general representation of all normal extensions of a formally normal minimal operator generated by a degenerate linear differential operator expression for first order, with linear selfadjoint operator coefficients, in the Hilbert space of vector functions on a finite interval is investigated in terms of boundary values. Similarly, if the Hilbert space is finite, all maximal hyponormal extensions of the hyponormal minimal operator produced by the given degenerate linear differential expression are expressed in the terms of boundary values. In addition, unlike the above, the representation of all normal extensions of the formal normal minimal operator produced by the singular degenerate linear differential expression for first order has been investigated in terms of boundary values. In addition, some spectrum problems of these extensions given with boundary value conditions for these three cases mentioned above are analyzed.