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Computational Methods and Function Theory

, Volume 12, Issue 2, pp 371–391 | Cite as

Matrix Representations of a Special Polynomial Sequence in Arbitrary Dimension

  • Isabel CaçãoEmail author
  • Maria Irene Falcão
  • Helmuth R. Malonek
Article

Abstract

This paper provides an insight into different structures of a special polynomial sequence of binomial type in higher dimensions with values in a Clifford algebra. The elements of the special polynomial sequence are homogeneous hypercomplex differentiable (monogenic) functions of different degrees and their matrix representation allows for their recursive construction in the same way as for complex power functions. This property can somehow be considered as a compensation for the loss of multiplicativity caused by the non-commutativity of the underlying algebra.

En]Keywords

monogenic function matrix representation 

2000 MSC

47A56 30G35 33C50 

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Copyright information

© Heldermann  Verlag 2012

Authors and Affiliations

  • Isabel Cação
    • 1
    Email author
  • Maria Irene Falcão
    • 2
  • Helmuth R. Malonek
    • 1
  1. 1.Department of Mathematics, Center for Research and Development in Mathematics and ApplicationsUniversity of AveiroAveiroPortugal
  2. 2.Department of Mathematics and ApplicationsUniversity of MinhoBragaPortugal

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