An analog of the trace formula for discrete Sturm-Liouville operators with asymptotically \(n\)-periodic coefficients
Let Nevai's class \(M\) of Jacobi matrices \[ J= \left[\begin{matrix} b_0 & a_1 & 0 & 0 &\cdot &\cdot &\cdot &\cdot\\ a_1 & b_1 & a_2 & 0 &\cdot &\cdot &\cdot &\cdot\\ 0 & a_2 & b_2 & a_3 &\cdot &\cdot &\cdot &\cdot\\ \cdot &\cdot &\cdot &\cdot &\cdot &\cdot &\cdot &\cdot\\ \cdot &\cdot &\cdot &\cdot &\cdot &\cdot &\cdot &\cdot\\ \cdot &\cdot &\cdot &\cdot &\cdot &\cdot &\cdot &\cdot\end{matrix}\right]\text{ such that }\underset{n\to\infty} {\text{lim}} a_n= 1/2,\text{ and }\underset{n\to \infty} {\text{lim}} b_n=0. \] In this paper, a connection between the Jacobi matrix \(J\) from the class \(M\) and the corresponding spectral measure is established.
scientific article; zbMATH DE number 1226011