  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.

Representation Theory;Analysis of PDEs