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

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

2012-04-16

arxiv.org/abs/1204.3613v2

Mathematics

Spectral Theory

Scientific paper

In this paper we investigate the one-dimensional Schrodinger operator L(q) with complex-valued periodic potential q when q\inL_{1}[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^{i2{\pi}nx}}. We prove that the Bloch eigenvalues are (2{\pi}n+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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