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pro vyhledávání: '"Faustino, Nelson"'
Autor:
Bernstein, Swanhild, Faustino, Nelson
This paper systematically investigates Paley-Wiener-type theorems in the context of hypercomplex variables. To this end, we introduce and study the so-called generalized Bernstein spaces endowed by the fractional Dirac operator $D_{\alpha}^{\theta}$
Externí odkaz:
http://arxiv.org/abs/2405.04989
Autor:
Faustino, Nelson, Marques, Jorge
We consider an integro-differential counterpart of the $\sigma-$evolution equation of the type \[ \partial_t^2 u(t,x)+\mu (-\Delta)^{\frac{\sigma}{2}} \partial_t u(t,x)+(-\Delta)^\sigma u(t,x)=f(t,x), \] with $\sigma>0$ and $\mu>0$, that encodes memo
Externí odkaz:
http://arxiv.org/abs/2212.10463
Autor:
Faustino, Nelson
In this paper we introduce a wide class of space-fractional and time-fractional semidiscrete Dirac operators of L\'evy-Leblond type on the semidiscrete space-time lattice $h\mathbb{Z}^n\times[0,\infty)$ ($h>0$), resembling to fractional semidiscrete
Externí odkaz:
http://arxiv.org/abs/2105.00355
Autor:
Faustino, Nelson
Publikováno v:
Mathematical Methods in the Applied Sciences (2021)
Starting from the pseudo-differential decomposition $\mathbf{D}=(-\Delta)^{\frac{1}{2}}\mathcal{H}$ of the Dirac operator $\displaystyle \mathbf{D}=\sum_{j=1}^n\mathbf{e}_j\partial_{x_j}$ in terms of the fractional operator $(-\Delta)^{\frac{1}{2}}$
Externí odkaz:
http://arxiv.org/abs/2104.01500
Autor:
Faustino, Nelson
In this paper we exploit the umbral calculus framework to reformulate the so-called discrete Cauchy-Kovalevskaya extension in the scope of hypercomplex variables. The key idea is to consider not only formal power series representation for the underly
Externí odkaz:
http://arxiv.org/abs/1802.08605
Autor:
Faustino, Nelson
Publikováno v:
S. Bernstein (ed.), Topics in Clifford Analysis, Trends in Mathematics, 2019
This paper presents an operational framework for the computation of the discretized solutions for relativistic equations of Klein-Gordon and Dirac type. The proposed method relies on the construction of an evolution-type operador from the knowledge o
Externí odkaz:
http://arxiv.org/abs/1801.09340
Autor:
Faustino, Nelson1,2 (AUTHOR) nelson.faustino@ymail.com
Publikováno v:
Mathematische Nachrichten. Jul2023, Vol. 296 Issue 7, p2758-2779. 22p.
Autor:
Faustino, Nelson
Publikováno v:
Math. Meth. Appl. Sci. 2017
Starting from the representation of the $(n-1)+n-$dimensional Lorentz pseudo-sphere on the projective space $\mathbb{P}\mathbb{R}^{n,n}$, we propose a method to derive a class of solutions underlying to a Dirac-K\"ahler type equation on the lattice.
Externí odkaz:
http://arxiv.org/abs/1602.02252
Autor:
Faustino, Nelson
Publikováno v:
Applied Mathematics and Computation, 2017
We present and study a new class of Fock states underlying to discrete electromagnetic Schr\"odinger operators from a multivector calculus perspective. This naturally lead to hypercomplex versions of Poisson-Charlier polynomials, Meixner polynomials,
Externí odkaz:
http://arxiv.org/abs/1505.05926
Autor:
Faustino, Nelson
Publikováno v:
Mathematical Methods in the Applied Sciences; Jul2024, Vol. 47 Issue 10, p7988-8001, 14p