关于广义Sublaplacian算子特征函数的展开

On the Eigenfunction Expansions for the Generalized Sublaplacian

本文研究了广义Ｓｕｂｌａｐｌａｃｉａｎ算子特征函数的展开．通过定义广义 －扭曲卷积，我们得到相应的Ｐｌａｎｃｈｅｒｅｌ定理及Ｈａｕｓｄｏｒｆｆ－Ｙｏｕｎｇ不等式，最后，我们还给出了当广义Ｓｕｂｌａｐｌａｃｉａｎ算子的特征值为离散时的一些结果．

In this paper, we investigate the eigenfunction expansions for the generalized Sublaplacian.By introducing the generalized -twisted convolutions, we obtain the Plancherel theorem and a Hausdorff-Young inequality. Some results are given under the condition that the eigenvalues of the generalized Sublaplacian are discrete.