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Higher-Order Szego Theorems With Two Singular Points
Barry Simon, Andrej Zlatos
We consider probability measures, $dμ=w(θ) \f{dθ}{2π} +dμ_\s$, on the unit circle, $\partial\bbD$, with Verblunsky coefficients, . We prove for i…
Sum Rules for Jacobi Matrices and Divergent Lieb-Thirring Sums
Andrej Zlatos
Extending earlier work of Killip-Simon and Simon-Zlatos, we obtain sum rules for Jacobi matrices in which the a.c. part of the spectral measure and the eigenvalues of the matrix ap…
Sparse Potentials With Fractional Hausdorff Dimension
Andrej Zlatos
We construct non-random bounded discrete half-line Schr\" odinger operators which have purely singular continuous spectral measures with fractional Hausdorff dimension (in some int…
The Szego Condition for Coulomb Jacobi Matrices
Andrej Zlatos
A Jacobi matrix with , and spectral measure satisfies the Szeg\H o condition if is finite.…
Sum Rules and the Szego Condition for Orthogonal Polynomials on the Real Line
Barry Simon, Andrej Zlatos
We study the Case sum rules, especially , for general Jacobi matrices. We establish situations where the sum rule is valid. Applications include an extension of Shohat's theor…