# Spectral theory of first-order systems: From crystals to Dirac operators

@article{BenArtzi2019SpectralTO, title={Spectral theory of first-order systems: From crystals to Dirac operators}, author={Matania Ben-Artzi and Tomio Umeda}, journal={Reviews in Mathematical Physics}, year={2019} }

Let [Formula: see text] be a constant coefficient first-order partial differential system, where the matrices [Formula: see text] are Hermitian. It is assumed that the homogeneous part is strongly propagative. In the non-homogeneous case it is assumed that the operator is isotropic. The spectral theory of such systems and their potential perturbations is expounded, and a Limiting Absorption Principle is obtained up to thresholds. Special attention is given to a detailed study of the Dirac and…

## 3 Citations

### Optimal Constants of Smoothing Estimates for the 2D Dirac Equation

- MathematicsJournal of Fourier Analysis and Applications
- 2022

In this paper, we discuss optimal constants and extremisers of Kato-smoothing estimates for the 2D Dirac equation. Smoothing estimates are inequalities that express the smoothing effect of dispersive…

### S ep 2 02 1 CONTINUUM LIMITS FOR DISCRETE DIRAC OPERATORS ON 2 D SQUARE LATTICES

- Mathematics
- 2021

We discuss the continuum limit of discrete Dirac operators on the square lattice in R as the mesh size tends to zero. To this end, we propose a natural and simple embedding of l(Z h ) into L(R) that…

### Continuum limits for discrete Dirac operators on 2D square lattices

- MathematicsArXiv
- 2021

A natural and simple embedding of l(Z h ) into L(R) that enables us to compare the discreteDirac operators with the continuum Dirac operators in the same Hilbert space L( R) is proposed and strong resolvent convergence is proved.

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