Teodorescu transform in the higher spin Clifford analysis
数学专题报告
报告题目(Title)：Teodorescu transform in the higher spin Clifford analysis
报告人(Speaker)：丁超教授 （安徽大学）
地点(Place)：后主楼1328
时间(Time)：2025年6月22日9：00-10:00
邀请人(Inviter)：汪志威
报告摘要
In theoretical physics, the Rarita-Schwinger equation is the relativisitic field
equation of spin-3/2 fermions. In 2002, Bures et al. generalized the Rarita-Schwinger
operator from spin-3/2 to arbitrary spin k/2 in the framework of Clifford analy
sis. The Rarita-Schwinger operator is considered as the generalization of Cauchy
Riemann operator in the higher spin cases, and many contributions has been done
in the so-called higher spin Clifford analysis since then. In this talk, we will in
troduce the Teodorescu transform in this context, which is the right inverse of the
Rarita-Schwinger operator. Norm estimates and mapping properties of the Teodor
escu transform will be discussed, and a Hodge decomposition will be introduced at
the end, which gives rise to the generalized Bergman space in the higher spin cases.
