A Strong Szego Theorem for Jacobi Matrices

E. Ryckman

doi:10.1007/s00220-007-0195-5

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A Strong Szego Theorem for Jacobi Matrices

E. Ryckman

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Abstract

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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BibTeX RIS

E. Ryckman. 2006-07-07. A Strong Szego Theorem for Jacobi Matrices. https://doi.org/10.1007/s00220-007-0195-5

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