On the spectra of infinite-dimensional Jacobi matrices
Jeffrey S. Geronimo · Journal of Approximation Theory · 1988
The Green's function method used by Case and Kac is extended to include unbounded Jacobi matrices. As a first application an upper bound on the number of eigenvalues is calculated, using the method of Bargmann. Another bound is found using the Birman-Schwinger argument, which is valid for matrix orthogonal polynomials.