Sharp estimates for the Opdam-Cherednik W-invariant heat kernel for the root system A1
Abstract
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 A1 with arbitrary multiplicity k>0. Sharp estimates of Opdam-Cherednik's radial heat kernel are conjectured for any root system.
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