Fabio Pizzichillo

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math.AP2019

Self-Adjointness of two dimensional Dirac operators on corner domains

Fabio Pizzichillo, Hanne Van Den Bosch

We investigate the self-adjointness of the two-dimensional Dirac operator $D$ , with quantum-dot and Lorentz-scalar $δ$ -shell boundary conditions, on piecewise $C^{2}$ domains with fi…

math.AP2018

A Hardy-type inequality and some spectral characterizations for the Dirac-Coulomb operator

Biagio Cassano, Fabio Pizzichillo, Luis Vega

We prove a sharp Hardy-type inequality for the Dirac operator. We exploit this inequality to obtain spectral properties of the Dirac operator perturbed with Hermitian matrix-valued…

math.AP2018

Boundary triples for the Dirac operator with Coulomb-type spherically symmetric perturbations

Biagio Cassano, Fabio Pizzichillo

We determine explicitly a boundary triple for the Dirac operator $H := - i α \cdot \nabla + m β + V (x)$ in $R^{3}$ , for $m \in R$ and $\mathbb V(x)= |x|^{-1} ( ν\mathb…