Sharp estimates of the spherical heat kernel

Abstract

We prove sharp two-sided global estimates for the heat kernel associated with a Euclidean sphere of arbitrary dimension.

A Central Limit Theorem for Gibbsian Invariant Measures of 2D Euler Equations

“…We nevertheless prefer to keep using the terminology of S 2 , for the sake of simplicity. We will make use of the following properties of the heat kernel p(t, x, y) = p(t, θ), for which we refer to [27,29].…”

Laplace Dirichlet heat kernels in convex domains

“…Above estimates have been complemented with asymptotics in [22], which revealed that the behaviour of p B (t, x, y) is in fact driven by the expression δ x+y 2 / √ t. A similar property will be observed in general lower bound (5). We refer the reader to [3,4,5,12,19,20,21] for some other recent articles focused on sharp estimates of heat kernels in other settings.…”

“…L in (20). Furthermore, adding also the condition W (τ 1 ) ∈ {0} × I 0 under the expectation we arrive at…”

Heat Kernel Approximation on Kendall Shape Space

“…Consequently, the heat kernel is appropriate for constructing nonlinear support vector machines for shapes' classification [43] . It is worth noting that to better grasp the significance of the heat kernel closed-form approximation in (11) it should be reminded that the straightforward resolution of heat equations is only feasible for a restricted set of classical manifolds [24][25][26][27] ; other approaches provide merely bounds of the heat kernel [28][29][30][31][32][33][34][35][36][37][38] . Furthermore, number of closed-form expressions have been proposed in the litterature to calculate the heat kernel on hyperspheres like k m S .…”