Expansions for the Dirac Operator and Related Operators in Super Spinor Space

摘要

In this paper, we study expansions for the Dirac operator D, the modified Dirac operator and the polynomial Dirac operator P(D) in super spinor space. These expansions are a meaningful generalization of the classical Almansi expansion in polyharmonic functions theory. As an application of the expansions, the generalized Riquier problem in super spinor space is investigated.