Publications

Last updated: December 16, 2025

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Nelson Faustino’s work is supported by CIDMA (https://ror.org/05pm2mw36) under the Portuguese Foundation for Science and Technology (FCT, https://ror.org/00snfqn58), Grants UID/04106/2025 (https://doi.org/10.54499/UID/04106/2025) and UID/PRR/04106/2025.

 


Since 2023
  1. (with Selma Negzaoui) A Novel Schwartz Space for the (k,2/n)-Generalized Fourier Transform (2025), Preprint
    arXiV: https://arxiv.org/abs/2507.04064

  2. (with Milton Ferreira, Uwe Kähler, Nelson Vieira) Hypercomplex Analysis and Its Applications – Extended Abstracts of the International Conference Celebrating Paula Cerejeiras’ 60th Birthday (2025). 
    URL: https://link.springer.com/book/9783031868573

  3. (with Swanhild Bernstein) Paley-Wiener Type Theorems
    Associated to Dirac Operators of Riesz-Feller type, J Fourier Anal Appl 31, 52 (2025). 
    DOI: https://doi.org/10.1007/s00041-025-10183-6
  4. On Discrete Conjugate Harmonic Functions in Hypercomplex Analysis. Complex Anal. Oper. Theory 19, 94 (2025). 
    DOI: https://doi.org/10.1007/s11785-025-01727-1
  5. (with Jorge Marques) Decay Estimates for Space-time Fractional Equations with Structural Damping and Nonlinear Memory, In book: New Tools in Mathematical Analysis and Applications (2025)
    DOI: 10.1007/978-3-031-77050-0_22
  6. On fundamental solutions of higher-order space-fractional Dirac equations, Mathematical Methods in the Applied Sciences, Volume 47, Issue 10, 15 July 2024, Pages 7988-8001
    DOI: 10.1002/mma.7714
  7. On fractional semidiscrete Dirac operators of Lévy-Leblond type
    Mathematische Nachrichten, Volume 296, Issue7 July 2023, Pages 2758-2779
    DOI: 10.1002/mana.202100234
     
    2011-2022
  8. (with Jorge Marques) Structurally damped σ−evolution equations with power-law memory (2022), Preprint.
    arXiV: https://arxiv.org/abs/2212.10463
  9. (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
  10. (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
  11. 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
  12. 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
  13. 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
  14. 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
  15. 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
  16. 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
  17. 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
  18. 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
  19. 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
  20. 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
  21. 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
  22. 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 
  23. 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.
  24. 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
  25. 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
  26. Discrete Dirac operators...
  27. Fischer Decomposition…
  28. 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
  29. 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
  30. 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