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In this research, the minimal and maximal operators defined by q- difference expression are given in the Hilbert space Lq² (0, ∞). The existence problem of a q−1-normal extension for the minimal operator is mentioned. In addition, the sets of the minimal operator spectrum and the maximal operator spectrum are examined. [ABSTRACT FROM AUTHOR]

In this paper, all normal extensions of the minimal operator associated with the singular degenerate linear differential expressions for first order in the Hilbert space of vector-functions are investigated in terms of boundary values. As well, it analyses the spectrum parts of any normal extension. [ABSTRACT FROM AUTHOR]

In this study, all maximal hyponormal extensions are given for the degenerate first order in the Hilbert space of vector-functions on a finite interval. The extensions are defined in terms of the boundary values. The structure of the spectrum of the maximal hyponormal extensions is also investigated. [ABSTRACT FROM AUTHOR]