Periodic Jacobi operators with complex coefficients
Vassilis G. Papanicolaou
National Technical University of Athens, Greece
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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 -th degree polynomial whose leading coefficient is is the Hill discriminant of finitely many discrete -periodic Schrödinger operators (Theorem 1). Also, in the case where the spectrum is a closed interval we prove a result (Theorem 2) which is the analog of Borg's Theorem for the non-self-adjoint Jacobi case.
Cite this article
Vassilis G. Papanicolaou, Periodic Jacobi operators with complex coefficients. J. Spectr. Theory 11 (2021), no. 2, pp. 781–819
DOI 10.4171/JST/357