Spectral Problems of a Class of Non-self-adjoint One-dimensional Schrodinger Operators

2012/04/16 by O. A. Veliev, Veliev, O. A.
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Numerical methods in inverse problems #Spectral Theory in Mathematical Physics #math.SP

paper · pdf · doi:10.48550/arxiv.1204.3613

arxiv created 2014/05/12 · arxiv updated 2014/05/13

Abstract

In this paper we investigate the one-dimensional Schrodinger operator L(q) with complex-valued periodic potential q when q\inL₁[0,1] and q_n=0 for n=0,-1,-2,..., where q_n are the Fourier coefficients of q with respect to the system e^i2πnx. We prove that the Bloch eigenvalues are (2πn+t)² for n\inZ, t\inC and find explicit formulas for the Bloch functions. Then we consider the inverse problem for this operator.

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