Clifford algebra-valued orthogonal polynomials in the open unit ball of Euclidean space

Fred Brackx, Nele De Schepper and Frank Sommen

International Journal of Mathematics and Mathematical Sciences, 2004, vol. 2004, 1-12

Abstract:

A new method for constructing Clifford algebra-valued orthogonal polynomials in the open unit ball of Euclidean space is presented. In earlier research, we only dealt with scalar-valued weight functions. Now the class of weight functions involved is enlarged to encompass Clifford algebra-valued functions. The method consists in transforming the orthogonality relation on the open unit ball into an orthogonality relation on the real axis by means of the so-called Clifford-Heaviside functions. Consequently, appropriate orthogonal polynomials on the real axis give rise to Clifford algebra-valued orthogonal polynomials in the unit ball. Three specific examples of such orthogonal polynomials in the unit ball are discussed, namely, the generalized Clifford-Jacobi polynomials, the generalized Clifford-Gegenbauer polynomials, and the shifted Clifford-Jacobi polynomials.

Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:713479

DOI: 10.1155/S0161171204401045

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