Remling's Theorem for vector-valued discrete Schrodinger operators

TL;DR

This paper generalizes Remling's Theorem to vector-valued discrete Schrödinger operators, demonstrating that the limit points of matrix potentials are reflectionless on the spectrum with full multiplicity.

Contribution

It extends a fundamental spectral theorem to the vector-valued case, providing new insights into the structure of matrix potentials in discrete Schrödinger operators.

Findings

Limit points of matrix potentials are reflectionless on the spectrum.

The theorem applies to vector-valued discrete Schrödinger operators.

Full multiplicity of the absolutely continuous spectrum is established.

Abstract

This paper extends Remling's Theorem to vector-valued discrete Schrodinger operators, showing that the {\omega} limit points of the matrix potentials, under the shift map, are reflectionless on the absolutely continuous spectrum with full multiplicity.