Browsing by Author "Pizzichillo, F."
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Boundary Triples for the Dirac Operator with CoulombType Spherically Symmetric Perturbations
Cassano, B.; Pizzichillo, F. (201902)We determine explicitly a boundary triple for the Dirac operator $H:=i\alpha\cdot \nabla + m\beta + \mathbb V(x)$ in $\mathbb R^3$, for $m\in\mathbb R$ and $\mathbb V(x)= x^{1} ( \nu \mathbb{I}_4 +\mu \beta i \lambda ... 
Dirac Operators and Shell Interactions: A Survey
OurmièresBonafos, T.; Pizzichillo, F. (20210101)In this survey we gather recent results on Dirac operators coupled with δshell interactions. We start by discussing recent advances regarding the question of selfadjointness for these operators. Afterwards we switch to ... 
A Hardytype inequality and some spectral characterizations for the DiracCoulomb operator
Cassano, B.; Pizzichillo, F.; Vega, L. (20190702)We prove a sharp Hardytype inequality for the Dirac operator. We exploit this inequality to obtain spectral properties of the Dirac operator perturbed with Hermitian matrixvalued potentials V of Coulomb type: we characterise ... 
A Hardytype inequality and some spectral characterizations for the Dirac–Coulomb operator
Cassano, B.; Pizzichillo, F.; Vega, L. (201906)We prove a sharp Hardytype inequality for the Dirac operator. We exploit this inequality to obtain spectral properties of the Dirac operator perturbed with Hermitian matrixvalued potentials $\mathbf V$ of Coulomb type: ... 
A Hardytype inequality and some spectral characterizations for the Dirac–Coulomb operator
Cassano, B.; Pizzichillo, F.; Vega, L. (20200101)We prove a sharp Hardytype inequality for the Dirac operator. We exploit this inequality to obtain spectral properties of the Dirac operator perturbed with Hermitian matrixvalued potentials V of Coulomb type: we characterise ... 
Klein's Paradox and the Relativistic $\delta$shell Interaction in $\mathbb{R}^3$
Mas, A.; Pizzichillo, F. (201711)Under certain hypothesis of smallness of the regular potential $\mathbf{V}$, we prove that the Dirac operator in $\mathbb{R}^3$ coupled with a suitable rescaling of $\mathbf{V}$, converges in the strong resolvent sense ... 
The relativistic spherical $\delta$shell interaction in $\mathbb{R}^3$: spectrum and approximation
Mas, A.; Pizzichillo, F. (20170803)This note revolves on the free Dirac operator in $\mathbb{R}^3$ and its $\delta$shell interaction with electrostatic potentials supported on a sphere. On one hand, we characterize the eigenstates of those couplings by ... 
SelfAdjoint Extensions for the Dirac Operator with CoulombType Spherically Symmetric Potentials
Cassano, B.; Pizzichillo, F. (2018)We describe the selfadjoint realizations of the operator $H:=i\alpha\cdot \nabla + m\beta + \mathbb V(x)$, for $m\in\mathbb R $, and $\mathbb V(x)= x^{1} ( \nu \mathbb{I}_4 +\mu \beta i \lambda \alpha\cdot{x}/{x}\,\beta)$, ... 
Selfadjointness of twodimensional Dirac operators on corner domains
Pizzichillo, F.; Van Den Bosch, H. (20210101)We investigate the selfadjointness of the twodimensional Dirac operator D, with quantumdot and Lorentzscalar ishell boundary conditions, on piecewise C2 domains (with finitely many corners). For both models, we prove ... 
Singular Perturbation of the Dirac Hamiltonian
Pizzichillo, F. (20171215)This thesis is devoted to the study of the Dirac Hamiltonian perturbed by deltatype potentials and Coulombtype potentials. We analysed the deltashell interaction on bounded and smooth domains and its approximation by ... 
Spectral asymptotics for $\delta$interactions on sharp cones
OurmièresBonafos, T.; Pankrashkin, K.; Pizzichillo, F. (2017)We investigate the spectrum of threedimensional Schr\"odinger operators with $\delta$interactions of constant strength supported on circular cones. As shown in earlier works, such operators have infinitely many eigenvalues ...