A Spectral Equivalence for Jacobi Matrices

Details A Spectral Equivalence for Jacobi Matrices A Spectral Equivalence for Jacobi Matrices

2006-04-24

arxiv.org/abs/math/0604515v2

Mathematics

Spectral Theory

13 pages

Scientific paper

We use the classical results of Baxter and Gollinski-Ibragimov to prove a new spectral equivalence for Jacobi matrices on $l^2(\N)$. 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 $\sum_{k=n}^\infty b_k$ and $\sum_{k=n}^\infty (a_k^2 - 1)$ lie in $l^2_1 \cap l^1$ or $l^1_s$ for $s \geq 1$.

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