Spectral theory of Sturm-Liouville difference operators
This paper deals with eigenvalue problems for the discrete Sturm-Liouville problem \[ -\Delta(f\Delta y)(n)+q(n)y(n)=\lambda w(n)y(n) \] for \(n=1,\dots,k\). The authors present several classes of explicit self-adjoint Sturm-Liouville difference operator with either a non-Hermitian leading coefficient function, or a non-Hermitian potential function, or a non-definite weight function, or a non-self-adjoint boundary condition. It is shown that a discrete Sturm-Liouville problem admits a difference operator realization if and only if it does not have all complex numbers as eigenvalues. Spectral properties of self-adjoint Sturm-Liouville difference operators are studied.
scientific article; zbMATH DE number 5382424