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Gaussian bounds for the heat kernels on the ball and the simplex: classical approach

Volume 250 / 2020

Gerard Kerkyacharian, Pencho Petrushev, Yuan Xu Studia Mathematica 250 (2020), 235-252 MSC: 42C05, 35K08. DOI: 10.4064/sm180423-13-10 Published online: 29 July 2019


Two-sided Gaussian bounds are established for the weighted heat kernels on the unit ball and the simplex in ${\mathbb R}^d$ generated by classical differential operators whose eigenfunctions are algebraic polynomials.


  • Gerard KerkyacharianLPSM, CNRS-UMR 7599, and Crest
  • Pencho PetrushevDepartment of Mathematics
    University of South Carolina
    Columbia, SC 29208, U.S.A.
  • Yuan XuDepartment of Mathematics
    University of Oregon
    Eugene, OR 97403-1222, U.S.A.

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