64 citations · 73 across the 15 of their papers we have counts for
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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…
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}…
Fine Structure of the Zeros of Orthogonal Polynomials, I. A Tale of Two Pictures
Barry Simon
Mhaskar-Saff found a kind of universal behavior for the bulk structure of the zeros of orthogonal polynomials for large . Motivated by two plots, we look at the finer structure…
Aizenman's Theorem for Orthogonal Polynomials on the Unit Circle
Barry Simon
For suitable classes of random Verblunsky coefficients, including independent, identically distributed, rotationally invariant ones, we prove that if \[ \mathbb{E} \biggl(\int\frac…
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…
Orthogonal polynomials on the unit circle: New results
Barry Simon
We announce numerous new results in the theory of orthogonal polynomials on the unit circle.