Abstract
Discrete Clifford analysis is a higher dimensional discrete function theory, based on skew Weyl relations. The basic notions are discrete monogenic functions, i.e. Clifford algebra valued functions in the kernel of a discrete Dirac operator. In this paper, we introduce the discrete Fueter polynomials, which form a basis of the space of discrete spherical monogenics, i.e. discrete monogenic, homogeneous polynomials. Their definition is based on a Cauchy–Kovalevskaya extension principle. We present the explicit construction for this discrete Fueter basis, in arbitrary dimension m and for arbitrary homogeneity degree k.
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H. De Ridder acknowledges support by the institutional grant no.B/10675/02 of Ghent University (BOF).
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De Ridder, H., De Schepper, H. & Sommen, F. Fueter polynomials in discrete Clifford analysis. Math. Z. 272, 253–268 (2012). https://doi.org/10.1007/s00209-011-0932-5
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DOI: https://doi.org/10.1007/s00209-011-0932-5