Barry Simon, Andrej Zlatos
Published 2002-06-14Version 1
We study the Case sum rules, especially $C_0$, for general Jacobi matrices. We establish situations where the sum rule is valid. Applications include an extension of Shohat's theorem to cases with an infinite point spectrum and a proof that if $\lim n (a_n -1)=\alpha$ and $\lim nb_n =\beta$ exist and $2\alpha <\abs{\beta}$, then the Szeg\H{o} condition fails.
On the dimensions of the oscillator algebras induced by orthogonal polynomials
On Rotated CMV Operators and Orthogonal Polynomials on the Unit Circle
Hankel Determinant and Orthogonal Polynomials for a Perturbed Gaussian Weight: from Finite $n$ to Large $n$ Asymptotics
