I am completing a comprehensive look at the theory of orthogonal polynomials on the unit circle (OPUC; we will use OPRL for the real-line case). These two 500+-page volumes [124, 125] to appear inâ€¦ (More)

We discuss the proof of and systematic application of Caseâ€™s sum rules for Jacobi matrices. Of special interest is a linear combination of two of his sum rules which has strictly positive terms.â€¦ (More)

This is a comprehensive exposition of the classical moment problem using methods from the theory of finite difference operators. Among the advantages of this approach is that the Nevanlinna functionsâ€¦ (More)

We consider a selfadjoint operator, A , and a selfadjoint rank-one projection, P, onto a vector, 9, which is cyclic for A. In terms of the spectral measure dp;, we give necessary and sufficientâ€¦ (More)

Using control of the growth of the transfer matrices, we discuss the spectral analysis of continuum and discrete half-line SchrÃ¶dinger operators with slowly decaying potentials. Among our results weâ€¦ (More)

This is a comprehensive review of the uses of potential theory in studying the spectral theory of orthogonal polynomials. Much of the article focuses on the Stahlâ€“Totik theory of regular measures,â€¦ (More)

We study inverse spectral analysis for finite and semi-infinite Jacobi matrices H. Our results include a new proof of the central result of the inverse theory (that the spectral measure determinesâ€¦ (More)

We give new examples of discrete SchrÃ¶dinger operators with potentials taking finitely many values that have purely singular continuous spectrum. If the hull X of the potential is strictly ergodic,â€¦ (More)