Periodic Jacobi Operators with Complex Coefficients

2019/09/19 by Papanicolaou, Vassilis G.
#39A12 #39A70 #47B39 #FOS: Mathematics #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.1909.09206

Abstract

We present certain results on the direct and inverse spectral theory of the Jacobi operator with complex periodic coefficients. For instance, we show that any N-th degree polynomial whose leading coefficient is (-1)^N is the Hill discriminant of finitely many discrete N-periodic Schrödinger operators (Theorem 1). Also, in the case where the spectrum is a closed interval we prove a result (Theorem 5) which is the analog of Borg's Theorem for the non-self-adjoint Jacobi case.

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