We consider Chebyshev polynomials, T_n (z) T n (z), for infinite, compact sets e ⊂ R e⊂ R
(that is, the monic polynomials minimizing the\sup sup-norm,|| T_n|| _ e|| T n|| e, on ee). We …

We extend some remarkable recent results of Lubinsky and Levin-Lubinsky from [− 1, 1] to
allow discrete eigenvalues outside σ ess and to allow σ ess first to be a finite union of closed …

This is an extended version of my 2018 Heineman prize lecture describing the work for
which I got the prize. The citation is very broad, so this describes virtually all my work prior to …

Perhaps the most common theme in Fritz Gesztesy's broad opus is the study of problems
with periodic or almost periodic finite gap differential and difference equations, especially …

In this paper, we generalize Szegőʼs theorem for orthogonal polynomials on the real line to
infinite gap sets of Parreau–Widom type. This notion includes Cantor sets of positive …

We study solutions of three-term recurrence relations whose N-step transfer matrices belong
to the uniform Stolz class. In particular, we derive the first order of their uniform asymptotics …

Let e⊂R be a finite union of disjoint closed intervals. We study measures whose essential
support is e and whose discrete eigenvalues obey a 1/2-power condition. We show that a …

We prove bounds of the form∑ e∈ I∩ σ d (H) dist (e, σ e (H)) 1/2≤ L 1-norm of a
perturbation, where I is a gap. Included are gaps in continuum one-dimensional periodic …

We study Nevai's condition that for orthogonal polynomials on the real line,
K_n(x,x_0)^2K_n(x_0,x_0)^-1\,dρ(x)→x_0, where K n is the Christoffel–Darboux kernel. We …

We give explicit examples of unbounded Jacobi operators with a few gaps in their essential
spectrum. More precisely a class of Jacobi matrices whose absolutely continuous spectrum …