Two spectral equivalences for Jacobi matrices.

摘要

We use the classical results of Baxter and Golinskii-Ibragimov to prove some new spectral equivalences for Jacobi matrices on ℓ2( N ). 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 k=ninfinity bk and k=ninfinity ( a2k-1 ) lie in either ℓ21 , ℓ21∩ℓ1 , or ℓ1s for s ≥ 1. Here ℓps denotes the ℓp space with weight ns.