Spectral problems for generalized Jacobi matrices Original Research Article

A new class of generalized Jacobi matrices is introduced. Every proper real rational function is proved to be the m-function of a unique finite generalized Jacobi matrix. Moreover, every generalized Nevanlinna function m(·) which is a solution of a determinate indefinite moment problem turns out to be the m-function of a unique infinite generalized Jacobi matrix. The method we use is based on the step-by-step Schur process of solving the indefinite moment problem. The convergence of the sequence of subdiagonal Pade approximants for the corresponding Hamburger series is investigated.