Dirac Operators with Operator Data of Wigner-von Neumann Type

TL;DR

This paper investigates the spectral properties of half-line Dirac operators with Wigner-von Neumann type data, showing absence of singular continuous spectrum for finite sums and bounding the Hausdorff dimension for infinite sums.

Contribution

It provides new results on the spectral analysis of Dirac operators with Wigner-von Neumann type data, including explicit spectral set descriptions and Hausdorff dimension bounds.

Findings

Absence of singular continuous spectrum for finite sums of Wigner-von Neumann functions.

Explicit spectral set depending on decay and frequencies.

Hausdorff dimension bounds for the singular spectrum in infinite sums.

Abstract

We consider half-line Dirac operators with operator data of Wigner-von Neumann type. If the data is a finite linear combination of Wigner-von Neumann functions, we show absence of singular continuous spectrum and provide an explicit set containing all embedded pure points depending only on the Lp decay and frequencies of the operator data. For infinite sums of Wigner-von Neumann-like terms, we bound the Hausdorff dimension of the singular part of the spectrum.