02-324 Andrej Zlatos

The Szego Condition for Coulomb Jacobi matrices (67K, LaTeX 2e) Jul 25, 02

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Abstract. A Jacobi matrix with $a_n\to 1$, $b_n\to 0$ and spectral measure $\nu'(x)dx+d\nu_{sing}(x)$ satisfies the Szeg\H o condition if \[ \int_{0}^\pi \ln \bigl[ \nu'(2\cos\tht)\bigr]d\tht \] is finite. We prove that if \[ a_n\equiv 1+\frac \al n + O(n^{-1-\eps}) \qquad \qquad b_n\equiv \frac \be n +O(n^{-1-\eps}) \] with $2\al\ge |\be|$ and $\eps>0$, then the corresponding matrix is Szeg\H o.

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