A generalization of Fueter's theorem in Dunkl–Clifford analysis

References

• Fei , M , Cerejeiras , P and Kähler , U . 2009 . Fueter's theorem and its generalizations in Dunkl-Clifford analysis . J. Phys. A: Math. Theor. , 42 ( 39 ) 395209, 15pp
   Google Scholar
• Dunkl , CF . 1989 . Differential-difference operators associated to reflection groups . Trans. Am. Math. Soc. , 311 : 167 – 183 .
   Google Scholar
• Dunkl , CF and Xu , Y . 2001 . Orthogonal Polynomials of Several Variables , Cambridge : Cambridge University Press .
   Google Scholar
• Dunkl , CF . 1991 . Integral kernels with reflection group invariance . Can. J. Math. , 43 : 1213 – 1227 .
   Google Scholar
• Heckman , GJ . 1991 . An elementary approach to the hypergeometric shift operators of Opdam . Invent. Math. , 103 : 341 – 350 .
   Google Scholar
• van Diejen , JF and Vinet , L . 2000 . “ Calogero-Moser-Sutherland Models ” . In CRM Series in Mathematical Physics , New York : Springer-Verlag .
   Google Scholar
• Rösler , M . 2003 . “ Dunkl Operators: Theory and Applications ” . In Orthogonal Polynomials and Special Functions (Leuven, 2002), Lecture Notes in Mathematics, Vol. 1817 , 93 – 135 . Berlin : Springer .
   Google Scholar
• Peña Peña , D and Sommen , F . 2010 . Fueter's theorem: The saga continues . J. Math. Anal. Appl. , 365 : 29 – 35 .
   Google Scholar
• Sommen , F . 2000 . On a generalization of Fueter's theorem . Z. Anal. Anwend. , 19 ( 4 ) : 899 – 902 .
   Google Scholar
• Brackx , F , Delanghe , R and Sommen , F . 1982 . “ Clifford Analysis ” . In Research Notes in Mathematics , Vol. 76 , Boston : Pitman Advanced Publishing Company .
   Google Scholar
• Delanghe , R , Sommen , F and Souček , V . 1992 . “ Clifford Algebra and Spinor Valued Functions: ” . In A Function Theory for Dirac Operator , Dordrecht : Kluwer .
   Google Scholar
• Cerejeiras , P , Kähler , U and Ren , G . 2006 . Clifford analysis for finite reflection groups . Complex Var. Elliptic Eqns. , 51 ( 5–6 ) : 487 – 495 .
   Google Scholar
• Peña Peña , D . 2008 . “ Cauchy-Kowalevski extensions, Fueter's theorems and boundary values of special systems in Clifford analysis ” . In Ph.D. thesis , University of Ghent .
   Google Scholar
• Ren , G . 2005 . Almansi decomposition for Dunkl operators . Sci. China Ser. A , 48 : 333 – 342 .
   Google Scholar
• Bernardes , G , Cerejeiras , P and Kähler , U . 2009 . Fischer decomposition and Cauchy kernel for Dunkl–Dirac operators . Adv. Appl. Clifford Algebra , 19 : 163 – 171 .
   Google Scholar