A Strong Szego Theorem for Jacobi Matrices

Details A Strong Szego Theorem for Jacobi Matrices A Strong Szego Theorem for Jacobi Matrices

2006-04-21

arxiv.org/abs/math/0604478v2

Mathematics

Spectral Theory

26 pages

Scientific paper

We use a classical result of Gollinski and Ibragimov to prove an analog of the strong Szego theorem 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 $l^2_1$, the linearly-weighted $l^2$ space.

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