Publications

Thesis:

T. N. Faustino, ”Discrete Clifford Analysis”, Ph.D thesis, Universidade de Aveiro , pp ix+130, (Aveiro, Portugal, 2009).

URL: http://biblioteca.sinbad.ua.pt/teses/2009001006

Publications in Math Sci Net:

1. N. Faustino, K. Gürlebeck, A. Hommel, U. Kähler, “Difference potentials for the Navier-Stokes equations in unbounded domains”, Journal for Difference Equations and Applications, 12, 2006, 577-596.

URL: http://www.ingentaconnect.com/content/tandf/gdea/2006/00000012/00000006/art00005

2. N. Faustino, U. Kähler, “Fischer Decomposition for Difference Dirac Operators”, Advances in Applied Clifford Algebras, 17, no.1, 2007, 37-58.

URL: http://www.springerlink.com/content/k353132603v74n46

3. N. Faustino, N. Vieira, “Numerical Clifford Analysis for nonlinear Schroedinger Problem”, International Conference of Numerical Analysis and Applied Mathematics. AIP Conference Proceedings, Volume 936, pp. 742-745 (2007).

URL: http://adsabs.harvard.edu/abs/2007AIPC..936..742F

4. N. Faustino, U. Kähler, F. Sommen, “Discrete Dirac Operators in Clifford Analysis”, Advances in Applied Clifford Algebras, 17, no.3, 2007, 451-467.

URL: http://www.springerlink.com/content/j58382q42524r204

5. P. Cerejeiras, N. Faustino, N. Vieira, Numerical Clifford Analysis for the Non-stationary Schrödinger Equation, Numerical Methods for Partial Differential Equations, Vol. 24, no.4, 2008, 1181 – 1202.

URL: http://www3.interscience.wiley.com/journal/117864646/abstract

6. N. Faustino, “The application of a discrete function theory to the solution of the Navier-Stokes equations”, Advances in Applied Clifford Algebras, Vol. 18, nºs 3,4, 2008, pp.599-610

URL: http://www.springerlink.com/content/x925880x6042223n/

7. N. Faustino, “Further results in discrete Clifford analysis, Progress in Analysis and Its Applications” - Proceedings of the 7th International ISAAC Congress, (M. Ruzhansky, J. Wirth eds.), World Scientific, pp. 205–211, (2010),

URL: http://eproceedings.worldscinet.com/9789814313179/9789814313179_0027.html

8. D. Constales, N. Faustino, R.S. Krausshar “Fock spaces, Landau operators and the time-harmonic Maxwell equations.”, J. Phys. A 2011: Math. Theor. 44 135303.

URL: http://iopscience.iop.org/1751-8121/44/13/135303

9. N. Faustino, G. Ren, “(Discrete) Almansi type decompositions: an umbral calculus framework based on osp(1|2) symmetries.”, Mathematical Methods in the Applied Sciences, Volume 34, Issue 16, pages 1961–1979, November 2011.

URL: http://onlinelibrary.wiley.com/doi/10.1002/mma.1498/abstract

Publications in Conference Proceedings with Referee:

i. N. Faustino, “Fischer Decomposition for Difference Dirac Operators”, 17th International Conference on the Application of Computer. Science and Mathematics in Architectur, K. Guerlebeck and C. Koenke, 1-10, Weimar 2006.

URL: http://euklid.bauing.uni-weimar.de/templates/papers/f86.pdf

ii. N. Faustino, “Interpolating Wavelets applied to the Navier-Stokes equations”, Proceedings of Applied Mathematics and Mechanics, 6, 2006, 735-736.

URL: http://www3.interscience.wiley.com/cgi-bin/abstract/114084418

iii. P. Cerejeiras, N. Faustino, N. Vieira, “Clifford Analysis for nonlinear time-dependent problems”, International Conference on Computational and Mathematical Methods in Science and Engineering 2006, R. Criado et al, 196-203, Madrid, 2006.

Submitted/Accepted Papers

S01/2012. L.D. Abreu, N. Faustino, On Toeplitz Operators and Localization Operators (2012), submitted.
(In this short note, we have shown that the proof of M. Englis [cf. M. Englis, Trans. Am. Math Society (2009), 1039-1052] also fulfils for uniformly convergent windows belonging to the Fock space).

Research Reports:

R06/2006. N. Faustino, U. Kaehler, G. Teschke “A Wavelet Galerkin Scheme for the Navier Stokes Equations”, 2006.

URL: http://user.hs-nb.de/~teschke/ps/42.pdf
(Abridged version of paper ii.)

R06/2008. N. Faustino, U. Kähler “On a correspondence principle between discrete differential forms, graph structure and multi-vector calculus on symmetric lattices”, 2008.

URL: http://uk.arxiv.org/abs/0712.1004
(Sept. 2011: We are still revisiting this version. Parts of it will be incorporated in two forthcoming manuscripts).

R01/2009. G. Ren, N. Faustino, “Almansi Theorems in Umbral Clifford Analysis and the Quantum Harmonic Oscillator”, 2009

URL: arXiv:0901.4691v1
(This manuscript corresponds to the reference 7. enclosed on paper iv. Most of the results enclosed on this version were improved and incorporated on the research paper S02/2011).

R07/2011. N. Faustino, ”Localization and Toeplitz Operators on Polyanalytic Fock Spaces”, 2011.

URL: http://arxiv.org/abs/1107.4680
(Nov. 2011: This preprint is not intended for publication. Parts of it will be incorporated in forthcoming manuscripts; The forthcoming paper P10/2011 will explore in depth the structure of the operators enclosed on this paper).

In Preparation:

P10/2011. N. Faustino, ”Vector-valued coherent states on polyanalytic Fock spaces related with Berezin-Klauder-Toeplitz quantization”

(This paper intends to give a wide interpretation for the framework used in S07/2011 by means of vector coherent states resp. vector squeezed states underlying the Heisenberg group resp. the metaplectic group). [Postponed]

P12/2011. N. Faustino, ”Landau-Weyl approach for hypercomplex variables“, International Conference of Numerical Analysis and Applied Mathematics, AIP Conference Proceedings. [Postponed]

URL: http://proceedings.aip.org/
(In this paper we will sift the results of paper P10/2012 for hypercomplex variables with the purpose of cleaning up most of the group theoretical aspects hidden on paper 7. )