Clifford algebra-valued orthogonal polynomials in the open unit ball of Euclidean space
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 func...
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| Format: | Article |
| Language: | English |
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Wiley
2004-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171204401045 |
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| _version_ | 1832547411591954432 |
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| author | Fred Brackx Nele De Schepper Frank Sommen |
| author_facet | Fred Brackx Nele De Schepper Frank Sommen |
| author_sort | Fred Brackx |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-15e70b86f16343ca9e594170c4df8739 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2004-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-15e70b86f16343ca9e594170c4df87392025-02-03T06:44:49ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252004-01-012004522761277210.1155/S0161171204401045Clifford algebra-valued orthogonal polynomials in the open unit ball of Euclidean spaceFred Brackx0Nele De Schepper1Frank Sommen2Clifford Research Group, Department of Mathematical Analysis, Ghent University, Galglaan 2, Gent 9000, BelgiumClifford Research Group, Department of Mathematical Analysis, Ghent University, Galglaan 2, Gent 9000, BelgiumClifford Research Group, Department of Mathematical Analysis, Ghent University, Galglaan 2, Gent 9000, BelgiumA 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.http://dx.doi.org/10.1155/S0161171204401045 |
| spellingShingle | Fred Brackx Nele De Schepper Frank Sommen Clifford algebra-valued orthogonal polynomials in the open unit ball of Euclidean space International Journal of Mathematics and Mathematical Sciences |
| title | Clifford algebra-valued orthogonal polynomials in the open unit ball of Euclidean space |
| title_full | Clifford algebra-valued orthogonal polynomials in the open unit ball of Euclidean space |
| title_fullStr | Clifford algebra-valued orthogonal polynomials in the open unit ball of Euclidean space |
| title_full_unstemmed | Clifford algebra-valued orthogonal polynomials in the open unit ball of Euclidean space |
| title_short | Clifford algebra-valued orthogonal polynomials in the open unit ball of Euclidean space |
| title_sort | clifford algebra valued orthogonal polynomials in the open unit ball of euclidean space |
| url | http://dx.doi.org/10.1155/S0161171204401045 |
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