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Matrix Representations of a Special Polynomial Sequence in Arbitrary Dimension

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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.

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Authors and Affiliations

  1. Department of Mathematics, Center for Research and Development in Mathematics and Applications, University of Aveiro, Campus Universitário de Santiago, 3810-193, Aveiro, Portugal

    Isabel Cação & Helmuth R. Malonek

  2. Department of Mathematics and Applications, University of Minho, Campus de Gualtar, 4710-057, Braga, Portugal

    Maria Irene Falcão

Authors
  1. Isabel Cação
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  2. Maria Irene Falcão
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  3. Helmuth R. Malonek
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Correspondence to Isabel Cação.

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Dedicated to Nick Papamichael

This work was supported by FEDER founds through COMPETE-Operational Programme Factors of Competitiveness (“Programa Operacional Factores de Competitividade”) and by Portuguese funds through the Center for Research and Development in Mathematics and Applications (University of Aveiro) and the Portuguese Foundation for Science and Technology (“FCT-Fundação para a Ciência e a Tecnologia”), within project PEst-C/MAT/UI4106/2011with COMPETE number FCOMP-01-0124-FEDER-022690.

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Cação, I., Falcão, M.I. & Malonek, H.R. Matrix Representations of a Special Polynomial Sequence in Arbitrary Dimension. Comput. Methods Funct. Theory 12, 371–391 (2012). https://doi.org/10.1007/BF03321833

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