标题： Opdam-Cherednik$W$-不变热核在根系$A_1$的精确估计 显示英文标题

标题： Sharp estimates for the Opdam-Cherednik $W$-invariant heat kernel for the root system $A_1$

摘要： 对于曲黎曼空间的非中心Weyl群不变热核以及Opdam-Cherednik拉普拉斯算子，首次系统地研究了其估计值。 我们证明了根系$A_1$在任意重数$k>0$下的精确估计。 对任何根系，Opdam-Cherednik的径向热核的精确估计被提出猜想。 显示英文摘要

摘要： For the first time, the estimates of the non-centered Weyl-group invariant heat kernel for curved Riemannian spaces and for Opdam-Cherednik Laplacians are studied systematically. We prove sharp estimates for the root system $A_1$ with arbitrary multiplicity $k>0$. Sharp estimates of Opdam-Cherednik's radial heat kernel are conjectured for any root system.