Fueter polynomials in discrete Clifford analysis

• DOI: 10.1007/s00209-011-0932-5
• Publication Date: 2011-09-08T07:36:09Z
• Authors: H. De Ridder; H. De Schepper; F. Sommen
• Keywords: Fueter polynomials; Mathematics and Statistics; Discrete Clifford analysis; 0101 mathematics; 01 natural sciences

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.