29 citations · 122 across the 17 of their papers we have counts for
18 papers
Gauge Transforms and Strichartz Estimates for Benjamin--Ono-Type Dirac Equations
Nelson Faustino
For , we consider the Benjamin--Ono-type Dirac equation where $(-Δ)…
Structurally damped evolution equations with power-law memory
Nelson Faustino, Jorge Marques
We consider an integro-differential counterpart of the evolution equation of the type \[ \partial_t^2 u(t,x)+μ(-Δ)^{\fracσ{2}} \partial_t u(t,x)+(-Δ)^σu(t,x)=f(t,x), \] with $σ…
On fractional semidiscrete Dirac operators of Lévy-Leblond type
Nelson Faustino
In this paper we introduce a wide class of space-fractional and time-fractional semidiscrete Dirac operators of Lévy-Leblond type on the semidiscrete space-time lattice $h\mathbb{Z…
On Fundamental Solutions of Higher-Order Space-Fractional Dirac equations
Nelson Faustino
Starting from the pseudo-differential decomposition of the Dirac operator $\displaystyle \mathbf{D}=\sum_{j=1}^n\mathbf{e}_j\partial_{x_j…
Time-changed Dirac-Fokker-Planck equations on the lattice
N. Faustino
A time-changed discretization for the Dirac equation is proposed. More precisely, we consider a Dirac equation with discrete space and continuous time perturbed by a time-dependent…
A note on the discrete Cauchy-Kovalevskaya extension
Nelson Faustino
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 t…
Relativistic Wave Equations on the lattice: an operational perspective
Nelson Faustino
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…
Hypercomplex Fock States for Discrete Electromagnetic Schrödinger Operators: A Bayesian Probability Perspective
Nelson Faustino
We present and study a new class of Fock states underlying to discrete electromagnetic Schrödinger operators from a multivector calculus perspective. This naturally lead to hyperco…
Solutions for the Klein-Gordon and Dirac equations on the lattice based on Chebyshev polynomials
Nelson Faustino
The main goal of this paper is to adopt a multivector calculus scheme to study finite difference discretizations of Klein-Gordon and Dirac equations for which Chebyshev polynomials…
Classes of hypercomplex polynomials of discrete variable based on the quasi-monomiality principle
Nelson Faustino
With the aim of derive a quasi-monomiality formulation in the context of discrete hypercomplex variables, one will amalgamate through a Clifford-algebraic structure of signature $(…
Special Functions of Hypercomplex Variable on the Lattice Based on SU(1,1)
Nelson Faustino
Based on the representation of a set of canonical operators on the lattice , which are Clifford-vector-valued, we will introduce new families of special functions of…
Localization and Toeplitz Operators on Polyanalytic Fock Spaces
Nelson Faustino
The well know conjecture of {\it Coburn} [{\it L.A. Coburn, {On the Berezin-Toeplitz calculus}, Proc. Amer. Math. Soc. 129 (2001) 3331-3338.}] proved by {\it Lo} [{\it M-L. Lo, {Th…
(Discrete) Almansi Type Decompositions: An umbral calculus framework based on symmetries
Nelson Faustino, Guangbin Ren
We introduce the umbral calculus formalism for hypercomplex variables starting from the fact that the algebra of multivariate polynomials $\BR[\underline{x}]$ shall be described in…
Fock Spaces, Landau Operators and the Regular Solutions of time-harmonic Maxwell equations
Denis Constales, Nelson Faustino, Soeren Krausshar
We investigate the representations of the solutions to Maxwell's equations based on the combination of hypercomplex function-theoretical methods with quantum mechanical methods. Ou…
Almansi Theorems in Umbral Clifford Analysis and the Quantum Harmonic Oscillator
Guangbin Ren, Nelson Faustino
We introduce the Umbral calculus into Clifford analysis starting from the abstract of the Heisenberg commutation relation . The Umbral Clifford analys…
On a correspondence principle between discrete differential forms, graph structure and multi-vector calculus on symmetric lattices
Nelson Faustino, Uwe Kaehler
Based on \cite{DH94}, we introduce a bijective correspondence between first order differential calculi and the graph structure of the symmetric lattice that allows one to encode co…
Numerical Clifford Analysis for Nonlinear Schrodinger Problem
P. Cerejeiras, N. Faustino, N. Vieira
The aim of this work is to study the numerical solution of the nonlinear Schrodinger problem using a combination between Witt basis and finite difference approximations. We constru…
Fischer Decomposition for Difference Dirac Operators
Nelson Faustino, Uwe Kaehler
We establish the basis of a discrete function theory starting with a Fischer decomposition for difference Dirac operators. Discrete versions of homogeneous polynomials, Euler and G…