二步幂零Lie群上sub-Laplace算子的谱

On Spectrum of the sub Laplacian on Two Step Nilpotent Lie Group

本文首先研究包括Ｇｒｅｉｎｅｒ算子和二步幂零Ｌｉｅ群上ｓｕｂＬａｐｌａｃｅ算子Ｌ在内的广义齐次线性偏微分算子的谱，然后利用酉表示理论确定了算子Ｌ的谱结构，并深化了Ｋ．Ｆｕｒｕｔａｎｉ，Ｋ．Ｓａｇａｍｉ，Ｎ．Ｏｔｓｕｋｉ关于Ｌａｐｌａｃｅ算子的有关结果．

In this paper we consider the spectrum of a class of generalized homogeneous linear partial differential operators including Greiner's operator and the sub Laplacian L on the two step nilpotent Lie group, then give the spectral structure of L by using the unitary representation theory. The related result of K. Furutani et al for Laplacian is deepened.