Pubblications

Preprints

• M. Camarasa, F. Pizzichillo: “Dirac operators with infinite mass boundary conditions on unbounded domains with infinite corners”.
  ArXiv preprint: 2312.12983, (2023).

Articles (accepted or published)

• J. Dolbeault, D. Gontier, F. Pizzichillo, H. Van Den Bosch: “Keller and Lieb-Thiering estimates of the eigenvalues in the gap of Dirac operators”.
  Revista Matemática Iberoamericana (2024); doi: 10.4171/RMI/1443
  

• M. Gallone, B. Cassano, F. Pizzichillo: “Dirac-Coulomb operators with infinite mass boundary conditions in sectors”.
  Journal of Mathematical Physics, (2022); doi: 10.1063/5.0089526
  

• F. Pizzichillo, H. Van Den Bosch: “Self-Adjointness of two dimensional Dirac operators on corner domains”.
  Journal of Spectral Theory, (2021); doi: 10.4171/jst/365
  

• T. Ourmières-Bonafos, F. Pizzichillo: “Dirac operators and shell interactions: a survey”.
  Mathematical Challenges of Zero-Range Physics. Springer INdAM Series, (2021); doi: 10.1007/978-3-030-60453-0_5
  

• B. Cassano, F. Pizzichillo, L. Vega: “A Hardy-type inequality and some spectral characterizations for the Dirac-Coulomb operator”.
  Revista Matemática Complutense, (2020); doi: 10.1007/s13163-019-00311-4
  

• B. Cassano, F. Pizzichillo: “Boundary triples for the Dirac operator with Coulomb-type spherically symmetric perturbations”.
  Journal of Mathematical Physics (2019); doi: 10.1063/1.5063986
  

• B. Cassano, F. Pizzichillo: “Self-adjoint extensions for the Dirac operator with Coulomb-type spherically symmetric potentials“.
  Letters in Mathematical Physics, (2018); doi: 10.1007/s11005-018-1093-9
  

• A. Mas, F. Pizzichillo: “Klein’s paradox and the relativistic $\delta$-shell interaction in $\mathbb R^3$“.
  Analysis & PDE, (2018); doi: 10.2140/apde.2018.11.705
  

• T. Ourmières-Bonafos, K. Pankrashkin, F. Pizzichillo: “Spectral asymptotics for $\delta$-interactions on sharp cones”.
  Journal of Mathematical Analysis and Applications, (2018); doi: 10.1063/1.5000381
  

• A. Mas, F. Pizzichillo: “The relativistic spherical $\delta$-shell interaction in $\mathbb R^3$: spectrum and approximations”.
  Journal of Mathematical Physics, (2017); doi: 10.1063/1.5000381
  

Thesis

• PhD Thesis: Singular perturbations for the Dirac Hamiltonian
  At BCAM – Basque Center for Applied Mathematics, under the supervision of Prof. Luis Vega.
  
  
• Master Thesis: Linear and non-linear damped wave equations.
  At University of Bari, under the supervision of Prof. Michael Reissig and Prof. Sandra Lucente.
  
  
• Bachelor Thesis: The spectral theorem for compact operators and applications to PDEs. (in italian).
  At University of Bari, under the supervision of Prof. Lorenzo D’Ambrosio .