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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.

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Sharp Estimates for the Opdam-Cherednik W-Invariant Heat Kernel for the Root System \(A_1\)

  • 会议论文

  • 发表日期：

    2025年

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  • P. Graczyk,
  • P. Sawyer

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.