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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 in , for and $\mathbb V(x)= |x|^{-1} ( ν\mathb…
math.AP2018
Sharp exponential localization for solutions of the Perturbed Dirac Equation
Biagio Cassano
We determine the largest non-trivial rate of exponential decay at infinity for solutions to the Dirac equation \begin{equation*} \mathcal{D}_n ψ+ \mathbb{V} ψ= 0 \quad \text{ in }\…