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18 papers · 1 filter
Schrodinger Operators with Purely Discrete Spectrum
Barry Simon
We prove has purely discrete spectrum if and, for all , and various extensions.
The Nevai Condition
Jonathan Breuer, Yoram Last, Barry Simon
We study Nevai's condition that for orthogonal polynomials on the real line, where is the CD kernel. We prove that it holds f…
Equilibrium measures and capacities in spectral theory
Barry Simon
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 Stahl-Totik theory of r…
Regularity and the Cesaro-Nevai class
Barry Simon
We consider OPRL and OPUC with measures regular in the sense of Ullman-Stahl-Totik and prove consequences on the Jacobi parameters or Verblunsky coefficients. For example, regulari…
Spectral and Dynamical Properties of Certain Random Jacobi Matrices with Growing Parameters
Jonathan Breuer
In this paper, a family of random Jacobi matrices, with off-diagonal terms that exhibit power-law growth, is studied. Since the growth of the randomness is slower than that of thes…
Weak convergence of CD kernels and applications
Barry Simon
We prove a general result on equality of the weak limits of the zero counting measure, , of orthogonal polynomials (defined by a measure ) and $\frac{1}{n} K_n(x,x) dμ(x)…