幂零矩阵群上的Wiener测度

Wiener measure for nilpotent matrix groups

利用Wiener测度与路径积分,Wiener对布朗运动做了完美的分析学描述.通过幂零矩阵群上次拉普拉斯算子的热核,定义了相应的Wiener测度,并且在其上建立了Wiener积分.然后,利用Wiener测度和Wiener积分给出了幂零矩阵群上薛定谔方程的解.

Wiener gave a characterization of the Brownian motion in term of Wiener measure.The Wiener measure on the nilpotent matrix group is established through the heat kernel corresponding to the sub-Laplacian,and the Wiener integral is defined.Then,the Feynman-Kac formula of the Schrodinger equation on nilpotent matrix groups is given.