Weyl-Titchmarsh type formula for discrete Schroedinger operator with Wigner-von Neumann potential

TL;DR

This paper derives a Weyl-Titchmarsh type formula for a discrete Schrödinger operator with a Wigner-von Neumann potential, linking spectral density to polynomial asymptotics, expanding understanding of spectral properties in such systems.

Contribution

It introduces a Weyl-Titchmarsh type formula for discrete Schrödinger operators with non-l^2 Wigner-von Neumann potentials, connecting spectral density to polynomial asymptotics.

Findings

Derived asymptotics of orthonormal polynomials for the operator.

Proved a Weyl-Titchmarsh type formula relating spectral density to polynomial coefficients.

Extended spectral analysis to non-l^2 Wigner-von Neumann potentials.

Abstract

We consider discrete Schroedinger operator J with Wigner-von Neumann potential not belonging to l^2. We find asymptotics of orthonormal polynomials associated to J. We prove the Weyl-Titchmarsh type formula, which relates the spectral density of J to a coefficient in asymptotics of orthonormal polynomials.