In the Pipeline

  1. On fractional semidiscrete Dirac operators of Lévy-Leblond type

  2. On fundamental solutions of higher-order space-fractional Dirac equations, Mathematical Methods in the Applied Sciences (online first on July 21, 2021)
    DOI: 10.1002/mma.7714 

  3. [New title] Non-Hermitian quadratic Hamiltonians encoding sl1(2)sl−1(2)

    DISCLAIMER: Currently, the aforementioned research papers are being [partially] supported by The Center for Research and Development in Mathematics and Applications (CIDMA) through the Portuguese Foundation for Science and Technology (FCT), references UIDB/04106/2020 and UIDP/04106/2020.

  4. (with Swanhild BernsteinA fractional Clifford Fourier Transform based on a deformed Hamiltonian for the harmonic oscillator, AIP Conference Proceedings 2293, 110002 (2020);
  5. Time-Changed Dirac–Fokker–Planck Equations on the LatticeJ Fourier Anal Appl 26, 44 (2020).
  6. Faustino, Nelson. 2019. “Relativistic Wave Equations on the Lattice: An Operational Perspective”. In Topics in Clifford Analysis, 439-469. Springer International Publishing.
    Publicado • 10.1007/978-3-030-23854-4_21
  7. Nelson Faustino. 2019. “A note on the discrete Cauchy-Kovalevskaya extension”. Mathematical Methods in the Applied Sciences.
  8. Faustino, Nelson. 2018. “Symmetry preserving discretization schemes through hypercomplex variables”. Trabalho apresentado em INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS (ICNAAM 2017)Salónica, Grécia, 020003-1-020003-4.
    Publicado • 10.1063/1.5043648
  9. N. Faustino. 2017. “Hypercomplex Fock states for discrete electromagnetic Schrödinger operators: A Bayesian probability perspective”. Applied Mathematics and Computation 315: 531-548.
  10. Nelson José Rodrigues Faustino. 2017. “A conformal group approach to the Dirac-Kähler system on the lattice”. Mathematical Methods in the Applied Sciences.
  11. Faustino, Nelson. 2016. “Solutions for the Klein–Gordon and Dirac Equations on the Lattice Based on Chebyshev Polynomials”. Complex Analysis and Operator Theory.
  12. Abreu, Luis Daniel; Faustino, Nelson. 2015. “ON TOEPLITZ OPERATORS AND LOCALIZATION OPERATORS”. Proceedings of the American Mathematical Society 143 (10): 4317-4323.
  13. Faustino, N.. 2014. “Classes of hypercomplex polynomials of discrete variable based on the quasi-monomiality principle”. Applied Mathematics and Computation 247: 607-622.
  14. Faustino, Nelson. 2013. “Special Functions of Hypercomplex Variable on the Lattice Based on SU(1,1)”. Symmetry Integrability and Geometry-Methods and Applications 9.
  15. Constales, Denis; Faustino, Nelson; Krausshar, Rolf Soeren. 2011. “Fock spaces, Landau operators and the time-harmonic Maxwell equations”. Journal of Physics a-Mathematical and Theoretical 44 (13).
  16. Faustino, N.; Ren, G.. 2011. “(Discrete) Almansi type decompositions: an umbral calculus framework based on DSP (1 vertical bar 2) symmetries”. Mathematical Methods in the Applied Sciences 34 (16): 1961-1979.


  17. Faustino, N.. 2010. “Further results in discrete Clifford analysis”. In Progress in Analysis and Its Applications7th International ISAAC CongressLondres, Reino Unido, 205-211. Singapura: WORLD SCIENTIFIC.
  18. Cerejeiras, P.; Faustino, N.; Vieira, N.. 2008. “Numerical Clifford analysis for nonlinear Schrodinger problem”. Numerical Methods For Partial Differential Equations 24 (4): 1181-1202.
  19. Faustino, Nelson. 2008. “The application of a discrete function theory to the solution of the Navier-Stokes equations”. Advances in Applied Clifford Algebras 18 (3-4): 599-610.
  20. Discrete Dirac operators...
  21. Fischer Decomposition…
  22. Faustino, N.; Vieira, N.; Simos, Theodore E.; Psihoyios, George; Tsitouras, Ch.. 2007. “Numerical Clifford Analysis for the Non-stationary Schro¨dinger Equation”. Trabalho apresentado em INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS (ICNAAM 2007)Corfu, Grécia, 742-746.
    Publicado • 10.1063/1.2790258
  23. Faustino, Nelson. 2006. “Interpolating Wavelets applied to the Navier-Stokes equations”. PAMM 6 (1): 735-736.
    Publicado • 10.1002/pamm.200610348
  24. Faustino, N; Gurlebeck, K; Hommel, A; Kahler, U. 2006. “Difference potentials for the Navier-Stokes equations in unbounded domains”. Journal of Difference Equations and Applications 12 (6): 577-595.

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