The tangential k-Cauchy-Fueter type operator and Penrose type integral formula on the generalized complex Heisenberg group  

作　　者：REN Guang-zhen SHI Yun KANG Qian-qian 

机构地区：[1]Department of Mathematics,Zhejiang International Studies University,Hangzhou 310023,China [2]Department of Mathematics,Zhejiang University of Science and Technology,Hangzhou 310023,China

出　　处：《Applied Mathematics(A Journal of Chinese Universities)》2024年第1期181-190,共10页高校应用数学学报（英文版）（B辑）

基　　金：Supported by National Nature Science Foundation in China(12101564,11971425,11801508);Nature Science Foundation of Zhejiang province(LY22A010013);Domestic Visiting Scholar Teacher Professional Development Project(FX2021042)。

摘　　要：The tangential k-Cauchy-Fueter operator and k-CF functions are counterparts of the tangential Cauchy–Riemann operator and CR functions on the Heisenberg group in the theory of several complex variables,respectively.In this paper,we introduce a Lie group that the Heisenberg group can be imbedded into and call it generalized complex Heisenberg.We investigate quaternionic analysis on the generalized complex Heisenberg.We also give the Penrose integral formula for k-CF functions and construct the tangential k-Cauchy-Fueter complex.

关 键 词：the generalized complex Heisenberg group the tangential k-Cauchy-Fueter type operator Penrose-type integral formula 

分 类 号：O177[理学—数学]