The quadratic of discrete Sturm-Liouville operators correct spectral issues for the handle

A number of problems in mathematics and physics, including the integration of Toda's equation, one of the basic equations of solid state mechanics, are brought to the study of inverse problems for the discrete Hill equation. Today, the relevance of this topic is growing due to the fact that this research has found important applications in quantum physics, the theory of linear and nonlinear specific product equations, crystallography, geological exploration. Such practical connections indicate the need to study discrete equations other than the discrete Hill equation, such as the inverse problems for the quadratic handle of discrete Sturm-Liouville operators.