A spectral equivalence for Jacobi matrices

摘要

We use the classical results of Baxter and Golinskii–Ibragimov to prove a new spectral equivalence for Jacobi matrices on . In particular, we consider the class of Jacobi matrices with conditionally summable parameter sequences and find necessary and sufficient conditions on the spectral measure such that Σ _k=n ~∞b_k and Σ _k=n ~∞(a_k~2-1) lie in l_1 ~2 for s≥1.