29 citations · 122 across the 17 of their papers we have counts for
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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…
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…
(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…
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…
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…