Bochner-Martinelli Formula for Higher Spin Operators of Several R^(6) Variables  

作　　者：Guangzhen REN Qianqian KANG 

机构地区：[1]Department of Mathematics,Zhejiang International Studies University,Hangzhou 310023,China

出　　处：《Chinese Annals of Mathematics,Series B》2023年第4期489-500,共12页数学年刊（B辑英文版）

基　　金：supported by the National Nature Science Foundation of China(Nos.12101564,11801508,11801523);the Nature Science Foundation of Zhejiang Province(No.LY22A010013)。

摘　　要：The higher spin operator of several R^(6)variables is an analogue of the■-operator in theory of several complex variables.The higher spin representation of so6(C)is⊙^(k)C_(4)and the higher spin operator D_(k) acts on⊙^(k)C_(4)-valued functions.In this paper,the authors establish the Bochner-Martinelli formula for higher spin operator Dk of several R^(6)variables.The embedding of R^(6n) into the space of complex 4n×4 matrices allows them to use two-component notation,which makes the spinor calculus on R^(6n)more concrete and explicit.A function annihilated by D_(k ) is called k-monogenic.They give the Penrose integral formula over R^(6n) and construct many k-monogenic polynomials.

关 键 词：Higher spin operator k-Monogenic Bochner-Martinelli formula Pen-rose integral formula 

分 类 号：O177[理学—数学]