关于高维抛物元和泊松核的定理

THE THEOREMS ON POISSON KERNEL IN H n+1 AND PARABOLIC ELEMENTS IN R n

讨论了高维抛物元和泊松核的关系，在一定限制条件下得到：设ｇ∈Ｍ（Ｒｎ），ｇ是抛物元，ｖ是ｇ的不动点，则对ｘ∈Ｈｎ＋１，Ｐ（ｘ，ｖ）ｓｉｎｈ１２ρ（ｘ，ｇｘ）是一个常数（由ｇ决定）．其中Ｐ（ｘ。

Applying the clifford matrix representation of M o ¨bius transformations in R n , we prove that if g is parabolic with fixed point v in R n then P(z,v) sinh12 ρ(z,gz) is constant (which depends on g ) where P(z,v) is the poisson Kernel in H n+1 .