Matrix approach to hypercomplex Appell polynomials
| Autor: | Graça Tomaz, Helmuth R. Malonek, Lidia Aceto |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2017 |
| Předmět: |
Pure mathematics
Polynomial Matrix representation Pascal matrix 010103 numerical & computational mathematics Appell polynomials 01 natural sciences Matrix (mathematics) 65F60 30G35 11B83 ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION Classical Analysis and ODEs (math.CA) FOS: Mathematics 0101 mathematics Complex Variables (math.CV) Mathematics Numerical Analysis Hypercomplex number Mathematics - Complex Variables Mathematics::Complex Variables Applied Mathematics 010102 general mathematics Clifford algebra Hypercomplex differentiability Function (mathematics) Nilpotent matrix Computational Mathematics Mathematics - Classical Analysis and ODEs Creation matrix |
| Zdroj: | Repositório Científico de Acesso Aberto de Portugal Repositório Científico de Acesso Aberto de Portugal (RCAAP) instacron:RCAAP |
| Popis: | Recently the authors presented a matrix representation approach to real Appell polynomials essentially determined by a nilpotent matrix with natural number entries. It allows to consider a set of real Appell polynomials as solution of a suitable first order initial value problem. The paper aims to confirm that the unifying character of this approach can also be applied to the construction of homogeneous Appell polynomials that are solutions of a generalized Cauchy–Riemann system in Euclidean spaces of arbitrary dimension. The result contributes to the development of techniques for polynomial approximation and interpolation in non-commutative Hypercomplex Function Theories with Clifford algebras. CIDMA – Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal; UDI/IPG – Research Unit for Inland Development, 6300-559 Guarda, Portugal |
| Databáze: | OpenAIRE |
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