Gaussian Bounds for the Weighted Heat Kernels on the Interval, Ball, and Simplex - Université Paris Cité Access content directly
Journal Articles Constructive Approximation Year : 2020

Gaussian Bounds for the Weighted Heat Kernels on the Interval, Ball, and Simplex

Abstract

Overview Stats Comments Citations 12 References 32 Related research 10 Download Share More The aim of this article is to establish two-sided Gaussian bounds for the heat kernels on the unit ball and simplex in $\mathbb{R}^n$, and in particular on the interval, generated by classical differential operators whose eigenfunctions are algebraic polynomials. To this end we develop a general method that employs the natural relation of such operators with weighted Laplace operators on suitable subsets of Riemannian manifolds and the existing general results on heat kernels. Our general scheme allows to consider heat kernels in the weighted cases on the interval, ball, and simplex with parameters in the full range.

Dates and versions

hal-03917001 , version 1 (31-12-2022)

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Cite

Gerard Kerkyacharian, Pencho Petrushev, Yuan Xu. Gaussian Bounds for the Weighted Heat Kernels on the Interval, Ball, and Simplex. Constructive Approximation, 2020, Constructive Approximation, 51 (1), pp.73-122. ⟨10.1007/s00365-019-09458-1⟩. ⟨hal-03917001⟩
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