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Monogenic Differential Operators

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Abstract

In this paper we consider operators acting on Clifford algebra valued polynomials and, in particular, differential operators with polynomial coefficients. The decomposition of polynomials into homogeneous pieces leads to the classical homogeneous decomposition of operators and the further decomposition of homogeneous polynomials into monogenic polynomials leads to the concept of monogenic operator. Monogenic operators are characterized in terms of commutation relations and the monogenic decomposition of differential operators is studied in detail.

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Authors and Affiliations

  1. Seminarie voor Algebra en, Functionaalanalyse - R.U.G., Galglaan 2, B-9000, Gent

    F. Sommen

  2. Seminarie voor Wiskundige, Analyse - R.U.G., Sint Pietersnieuwstraat 39, B-9000, Gent

    N. Acker

  3. Research Associate, NFWO, Belgium

    F. Sommen

Authors
  1. F. Sommen
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  2. N. Acker
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To Professor Klaus Habetha on the occasion of his 60th birthday

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Sommen, F., Acker, N. Monogenic Differential Operators. Results. Math. 22, 781–798 (1992). https://doi.org/10.1007/BF03323123

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  • DOI: https://doi.org/10.1007/BF03323123

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