TY - JOUR UR - http://lib.ugent.be/catalog/pug01:1938085 ID - pug01:1938085 LA - eng TI - Clifford-Gegenbauer polynomials related to the Dunkl Dirac operator PY - 2011 JO - (2011) BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETY-SIMON STEVIN SN - 1370-1444 PB - 2011 AU - De Bie, Hendrik TW16 002000066440 AU - De Schepper, Nele TW16 001997134313 AB - We introduce the so-called Clifford-Gegenbauer polynomials in the framework of Dunkl operators, as well on the unit ball B(1), as on the Euclidean space IR(m). In both cases we obtain several properties of these polynomials, such as a Rodrigues formula, a differential equation and an explicit relation connecting them with the Jacobi polynomials on the real line. As in the classical Clifford case, the orthogonality of the polynomials on IR(m) must be treated in a completely different way than the orthogonality of their counterparts on B(1). In case of IR(m), it must be expressed in terms of a bilinear form instead of an integral. Furthermore, in this paper the theory of Dunkl monogenics is further developed. ER -Download RIS file
00000nam^a2200301^i^4500 | |||
001 | 1938085 | ||
005 | 20180813141223.0 | ||
008 | 111029s2011------------------------eng-- | ||
022 | a 1370-1444 | ||
024 | a 000293200100001 2 wos | ||
024 | a 1854/LU-1938085 2 handle | ||
040 | a UGent | ||
245 | a Clifford-Gegenbauer polynomials related to the Dunkl Dirac operator | ||
260 | c 2011 | ||
520 | a We introduce the so-called Clifford-Gegenbauer polynomials in the framework of Dunkl operators, as well on the unit ball B(1), as on the Euclidean space IR(m). In both cases we obtain several properties of these polynomials, such as a Rodrigues formula, a differential equation and an explicit relation connecting them with the Jacobi polynomials on the real line. As in the classical Clifford case, the orthogonality of the polynomials on IR(m) must be treated in a completely different way than the orthogonality of their counterparts on B(1). In case of IR(m), it must be expressed in terms of a bilinear form instead of an integral. Furthermore, in this paper the theory of Dunkl monogenics is further developed. | ||
598 | a A1 | ||
100 | a De Bie, Hendrik u TW16 0 002000066440 0 801002044535 | ||
700 | a De Schepper, Nele u TW16 0 001997134313 0 801001539428 | ||
650 | a Mathematics and Statistics | ||
653 | a Clifford-Gegenbauer polynomials | ||
653 | a Dunkl monogenics | ||
653 | a Dunkl operators | ||
653 | a Clifford analysis | ||
653 | a WEIGHT | ||
653 | a BALL | ||
773 | t BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETY-SIMON STEVIN g Bull. Belg. Math. Soc.-Simon Stevin. 2011. 18 (2) p.193-214 q 18:2<193 | ||
856 | 3 Full Text u https://biblio.ugent.be/publication/1938085/file/1938086 z [open] y 2011_hdb_nds_Clifford-Gegenbauer_polynomials_related_to_the_Dunkl-Dirac_operator.pdf | ||
920 | a article | ||
Z30 | x EA 1 TW16 | ||
922 | a UGENT-EA |
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