Spectral problems for generalized Jacobi matrices (Q1826811)

The paper starts by the definition of a new class of generalized Jacobi matrices. Then it shows that every proper rational function is proved to be the \(m-\)function of a unique finite generalized Jacobi matrix. An analog of Stone's theorem that every cyclic self-adjoint operator in a Pontryagin space is unitarily equivalent to some generalized Jacobi matrix is given next. Finally, the convergence of the sequence of subdiagonal \(\left[ L-1/L \right] \) Padé approximants for the corresponding Hamburger series \( \sum\limits_{j=0}^{\infty }\left( -1\right) ^{j}s_{j}z^{j}\) is investigated.