Publications

Last update: April 11th, 2023 

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Author’s research is currently 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.

 

Since 2021 
  1. (with Jorge Marques) Structurally damped σ−σ−evolution equations with power-law memory (2022), Under Review.
    arXiV: https://arxiv.org/abs/2212.10463

     

  2. (with Jorge Marques) Strichartz estimates for structurally damped equations of space-time-fractional type, ICMA2SC’22 extended abstract (2022). DOI: http://dx.doi.org/10.34630/20734

     

  3. On fractional semidiscrete Dirac operators of Lévy-Leblond type
    Mathematische Nachrichten, (First published: 11 April 2023)
    DOI: 10.1002/mana.202100234

  4. On fundamental solutions of higher-order space-fractional Dirac equations, Mathematical Methods in the Applied Sciences (First published: 01 September 2021)
    DOI: 10.1002/mma.7714 

     

    2011-2020 
  5. (with Swanhild Bernstein) A fractional Clifford Fourier Transform based on a deformed Hamiltonian for the harmonic oscillator, AIP Conference Proceedings 2293, 110002 (2020); https://doi.org/10.1063/5.0027173

     

  6. Time-Changed Dirac–Fokker–Planck Equations on the Lattice. J Fourier Anal Appl 26, 44 (2020). https://doi.org/10.1007/s00041-020-09754-6

  7. Faustino, Nelson. 2019. “Relativistic Wave Equations on the Lattice: An Operational Perspective”. In Topics in Clifford Analysis, 439-469. Springer International Publishing. http://dx.doi.org/10.1007/978-3-030-23854-4_21.
    Publicado • 10.1007/978-3-030-23854-4_21

     

  8. Nelson Faustino. 2019. “A note on the discrete Cauchy-Kovalevskaya extension”. Mathematical Methods in the Applied Sciences. https://doi.org/10.1002/mma.5452.
    10.1002/mma.5452

     

  9. 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

     

  10. N. Faustino. 2017. “Hypercomplex Fock states for discrete electromagnetic Schrödinger operators: A Bayesian probability perspective”. Applied Mathematics and Computation 315: 531-548. https://doi.org/10.1016/j.amc.2017.07.080.
    10.1016/j.amc.2017.07.080

     

  11. Nelson José Rodrigues Faustino. 2017. “A conformal group approach to the Dirac-Kähler system on the lattice”. Mathematical Methods in the Applied Sciences. https://doi.org/10.1002%2Fmma.4291.
    10.1002/mma.4291

     

  12. Faustino, Nelson. 2016. “Solutions for the Klein–Gordon and Dirac Equations on the Lattice Based on Chebyshev Polynomials”. Complex Analysis and Operator Theory.
    10.1007/s11785-015-0476-5

     

  13. Abreu, Luis Daniel; Faustino, Nelson. 2015. “ON TOEPLITZ OPERATORS AND LOCALIZATION OPERATORS”. Proceedings of the American Mathematical Society 143 (10): 4317-4323. http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=ORCID&SrcApp=OrcidOrg&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=WOS:000364412600019&KeyUID=WOS:000364412600019.
    10.1090/proc/12211

     

  14. Faustino, N.. 2014. “Classes of hypercomplex polynomials of discrete variable based on the quasi-monomiality principle”. Applied Mathematics and Computation 247: 607-622.
    10.1016/j.amc.2014.09.027

     

  15. Faustino, Nelson. 2013. “Special Functions of Hypercomplex Variable on the Lattice Based on SU(1,1)”. Symmetry Integrability and Geometry-Methods and Applications 9.
    10.3842/SIGMA.2013.065

     

  16. 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).
    10.1088/1751-8113/44/13/135303

     

  17. 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.

    10.1002/mma.1498


    2006-2010 

     

  18. Faustino, N.. 2010. “Further results in discrete Clifford analysis”. In Progress in Analysis and Its Applications: 7th International ISAAC Congress, Londres, Reino Unido, 205-211. Singapura: WORLD SCIENTIFIC.
  19. Cerejeiras, P.; Faustino, N.; Vieira, N.. 2008. “Numerical Clifford analysis for nonlinear Schrodinger problem”. Numerical Methods For Partial Differential Equations 24 (4): 1181-1202.
    10.1002/num.20312

     

  20. 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.
    10.1007/s00006-008-0097-4

     

  21. Discrete Dirac operators...
  22. Fischer Decomposition…

     

  23. 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

     

  24. Faustino, Nelson. 2006. “Interpolating Wavelets applied to the Navier-Stokes equations”. PAMM 6 (1): 735-736. http://dx.doi.org/10.1002/pamm.200610348.
    Publicado • 10.1002/pamm.200610348

     

  25. 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.
    10.1080/10236190600637965

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