Greiner算子特征值的Yang不等式

Yang inequality for eigenvalues of the Greiner operator

将一些基本不等式与算子定理巧妙结合,得到了Greiner算子ΔL=∑nj=1(X2j+Y2j),其中Xj,Yj(j=1,…,n)是满足Hrmander条件的向量场)特征值的Yang不等式∑ki=1(λk+1-λi)2≤2n∑ki=1(λk+1-λi)λi,从而将欧氏空间上Laplace算子和HeisenbergLaplace算子特征值的Yang不等式推广到Greiner算子情形.还得到了Payne-Pólya-Weinberger型不等式λk+1-λk≤2nk∑ki=1λi和上界估计λk+1≤1+2()n1k(∑ki=1λi).

Abstract：The Yang inequalities of eigenvalues for the Greiner operator are established and several inter ested corollaries are obtained by combining some basic inequalities with operator theorems subtly. These results generalize ones for the Laplacian and the Heisenberg Laplacian. The Greiner operator is .