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- We consider a nonsymmetric first-order differential operator, where  P  is a 2 × 2 matrix whose components are in  L 2  (0 ,  1). We study an eigenvalue problem for  A  with boundary conditions at  x  = 0 ,  1. We establish an asymptotic form of the eigenvalues and prove that the set of the root vectors forms a Riesz basis in  {L 2  (0 ,  1) } 2  . Moreover we show some characterization of  L 2  -coefficients in an inverse eigenvalue problem. The key is a transformation formula.

Spectral properties and an inverse eigenvalue problem for non-symmetric systems of ordinary differential operators