A matrix recurrence for systems of Clifford algebra-valued orthogonal polynomials. (English) Zbl 1305.33028
Summary: Recently, the authors developed a matrix approach to multivariate polynomial sequences by using methods of hypercomplex function theory [Comput. Methods Funct. Theory 12, No. 2, 371–391 (2012; Zbl 1272.30069)]. 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.
MSC:
| 33C65 | Appell, Horn and Lauricella functions |
| 15A66 | Clifford algebras, spinors |
| 30G35 | Functions of hypercomplex variables and generalized variables |
Citations:
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