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A Matrix Recurrence for Systems of Clifford Algebra-Valued Orthogonal Polynomials

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Abstract

Recently, the authors developed a matrix approach to multivariate polynomial sequences by using methods of Hypercomplex Function Theory (Matrix representations of a basic polynomial sequence in arbitrary dimension. Comput. Methods Funct. Theory, 12 (2012), no. 2, 371-391). This paper deals with an extension of that approach to a recurrence relation for the construction of a complete system of orthogonal Clifford-algebra valued polynomials of arbitrary degree. At the same time the matrix approach sheds new light on results about systems of Clifford algebra-valued orthogonal polynomials obtained by Gürlebeck, Bock, Lávička, Delanghe et al. during the last five years. In fact, it allows to prove directly some intrinsic properties of the building blocks essential in the construction process, but not studied so far.

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Authors and Affiliations

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

    I. Cação & H. R. Malonek

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

    M. I. Falcão

Authors
  1. I. Cação
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  2. M. I. Falcão
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  3. H. R. Malonek
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Corresponding author

Correspondence to H. R. Malonek.

Additional information

Dedicated to Professor Klaus Gürlebeck on the occasion of his 60th birthday

This work was supported by Portuguese funds through the CIDMA - Center for Research and Development in Mathematics and Applications of the University of Aveiro, the CMAT - Research Centre of Mathematics of the University of Minho and the Portuguese Foundation for Science and Technology (“FCT - Fundação para a Ciência e a Tecnologia''), within projects PEst-OE/MAT/UI4106/2014 and PEstOE/MAT/UI0013/2014.

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Cação, I., Falcão, M.I. & Malonek, H.R. A Matrix Recurrence for Systems of Clifford Algebra-Valued Orthogonal Polynomials. Adv. Appl. Clifford Algebras 24, 981–994 (2014). https://doi.org/10.1007/s00006-014-0505-x

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  • DOI: https://doi.org/10.1007/s00006-014-0505-x

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