most citedFine Structure of the Zeros of Orthogonal Polynomials, I. A Tale of Two Pictures

64 citations · 73 across the 13 of their papers we have counts for

collaborators

13 papers

math.SP20051 cited

Jost functions and Jost solutions for Jacobi matrices, III. Asymptotic series for decay and meromorphicity

Barry Simon

We show that the parameters of a Jacobi matrix have a complete asymptotic series $ a_n^2 -1 &= \sum_{k=1}^{K(R)} p_k(n) μ_k^{-2n} + O(R^{-2n}) b_n &= \sum_{k=1}^{K(R)} p…

math.SP2005

The essential spectrum of Schrodinger, Jacobi, and CMV operators

Yoram Last, Barry Simon

We provide a very general result that identifies the essential spectrum of broad classes of operators as exactly equal to the closure of the union of the spectra of suitable limits…

math.SP2005

Meromorphic Szego functions and asymptotic series for Verblunsky coefficients

Barry Simon

We prove that the Szegő function, , of a measure on the unit circle is entire meromorphic if and only if the Verblunsky coefficients have an asymptotic expansion in exponenti…

math.SP2005

OPUC on One Foot

Barry Simon

We present an expository introduction to orthogonal polynomials on the unit circle.

math.SP2004

Fine structure of the zeros of orthogonal polynomials, III. Periodic recursion coefficients

Barry Simon

We discuss asymptotics of the zeros of orthogonal polynomials on the real line and on the unit circle when the recursion coefficients are periodic. The zeros on or near the absolut…

math.SP20045 cited

Fine Structure of the Zeros of Orthogonal Polynomials, II. OPUC With Competing Exponential Decay

Barry Simon

We present a complete theory of the asymptotics of the zeros of OPUC with Verblunsky coefficients where and $\abs{b_\ell}…