论文标题
$ su（2）$的全部修改的对数Sobolev不平等现象
Complete Modified Logarithmic Sobolev inequality for sub-Laplacian on $SU(2)$
论文作者
论文摘要
我们证明，$ su（2）上的规范子拉普拉斯式的$（2）$允许其所有矩阵值函数的统一修改后的Log-Sobolev不平等，而与矩阵维度无关。这是亚拉普拉斯的第一个例子，即已经获得了矩阵值修改的对数 - 贝贝尔夫不等式。我们还表明，在Lie组中，HEAT内核测量$ P_T $在时间$ t $允许矩阵价值修改的log-sobolev常数$ o（t^{ - 1}）$。
We prove that the canonical sub-Laplacian on $SU(2)$ admits a uniform modified log-Sobolev inequality for all its matrix-valued functions, independent of the matrix dimension. This is the first example of sub-Laplacian that a matrix-valued modified log-Sobolev inequality has been obtained. We also show that on Lie groups, the heat kernel measure $p_t$ at time $t$ admits matrix-valued modified log-Sobolev constants of order $O(t^{-1})$.
