Frantisek Stampach: On spectral properties of a class of complex Jacobi matrices with periodically modulated weights

Abstract

First part of the talk will be devoted to discussion of complex Jacobi matrices in general. First of all, we recall the construction of Jacobi operator from a given semi-infinite complex Jacobi matrix and show some standard tools that are important for its spectral analysis.

In the second part, we draw our attention to a concrete family of complex Jacobi matrices whose diagonal vanishes and the off-diagonal sequence depends on a complex parameter. We provide a detailed spectral analysis of these operators focusing on the non-self-adjoint case and the spectral phase transition phenomena.