Abstract
In this paper, by using the methods of the operator theory, the general form of all compactly solvable extension of the minimal operator which is generated by the first order linear differential operator expression in the Hilbert spaces of vector-functions on finite interval has been found. Later on, the spectrum set of the compactly solvable extensions has been investigated. In addition, the asymptotical behavior of the eigenvalues of any inverse of compactly solvable extension has been studied. Finally, the necessary and sufficient condition for the inverse of the compactly solvable extensions to be belong to Schatten–von Neumann classes has been given.
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