188 citations · 243 across the 4 of their papers we have counts for
12 papers
The Analytic Theory of Matrix Orthogonal Polynomials
David Damanik, Alexander Pushnitski, Barry Simon
We give a survey of the analytic theory of matrix orthogonal polynomials.
Perturbations of Orthogonal Polynomials With Periodic Recursion Coefficients
David Damanik, Rowan Killip, Barry Simon
We extend the results of Denisov-Rakhmanov, Szego-Shohat-Nevai, and Killip-Simon from asymptotically constant orthogonal polynomials on the real line (OPRL) and unit circle (OPUC)…
Jost Functions and Jost Solutions for Jacobi Matrices, II. Decay and Analyticity
David Damanik, Barry Simon
We present necessary and sufficient conditions on the Jost function for the corresponding Jacobi parameters and to have a given degree of exponential decay.
Jost Functions and Jost Solutions for Jacobi Matrices, I. A Necessary and Sufficient Condition for Szego Asymptotics
David Damanik, Barry Simon
We provide necessary and sufficient conditions for a Jacobi matrix to produce orthogonal polynomials with Szegő asymptotics off the real axis. A key idea is to prove the equivalenc…
Schroedinger Operators With Few Bound States
David Damanik, Rowan Killip, Barry Simon
We show that whole-line Schrödinger operators with finitely many bound states have no embedded singular spectrum. In contradistinction, we show that embedded singular spectrum is p…
Almost Everywhere Positivity of the Lyapunov Exponent for the Doubling Map
David Damanik, Rowan Killip
We show that discrete one-dimensional Schrödinger operators on the half-line with ergodic potentials generated by the doubling map on the circle, , may be realiz…