Algebraic Approach to Slice Monogenic Functions

作者：Cnudde Lander^*; De Bie Hendrik; Ren Guangbin

来源：Complex Analysis and Operator Theory, 2015, 9(5): 1065-1087.

DOI：10.1007/s11785-014-0393-z

• Slice Dirac operator
• Clifford-Hermite polynomials
• Slice monogenic functions

In recent years, the study of slice monogenic functions has attracted more and more attention in the literature. In this paper, an extension of the well-known Dirac operator is defined which allows to establish the Lie superalgebra structure behind the theory of slice monogenic functions. Subsequently, an inner product is defined corresponding to this slice Dirac operator and its polynomial null-solutions are determined. Finally, analogues of the Hermite polynomials and Hermite functions are constructed in this context and their properties are studied.

• 出版日期2015-6
• 单位中国科学技术大学