Let L denote the operator generated in L 2 (R + , E) by the differential expression l(y) = −y + Q(x)y, x ∈ R + , and the boundary condition (where Q is a matrix-valued function and A 0 , A 1 , B 0 , B 1 are non-singular matrices, with A 0 B 1 − A 1 B 0 = 0. In this paper, using the uniqueness theorems of analytic functions, we investigate the eigenvalues and the spectral singularities of L. In particular, we obtain the conditions on q under which the operator L has a finite number of the eigenvalues and the spectral singularities.

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