Asymptotics of the Heat Kernel on Rank 1 Locally Symmetric Spaces

Pointwise Lower Bounds on the Heat Kernels of Higher Order Schrödinger Operators

We apply Davies' method for obtaining pointwise lower bounds on the heat kernels of higher-order differential operators to obtain pointwise lower bounds in the presence of a polynomialy bounded potential.

紧致度量图对角线上的热核

The heat kernel on the diagonal for a compact metric graph

本文研究紧致度量图上热核的对角线限制，证明其满足修正热方程，并由此推导出边热迹公式及完全对称图的显式公式。

Pointwise Lower bounds on the Heat Kernels of Uniformally Elliptic Operators in Bounded Regions

We obtain pointwise lower bounds for heat kernels of higher order differential operators with Dirichlet boundary conditions on bounded domains in $\R^N$. The bounds exhibit explicitly the nature of the spatial decay of the heat kernel close to the boundary. We make no smoothness assumptions on our operator coefficients which we assume only to be bounded and measurable.

Gaussian Upper Bounds on Heat Kernels of Uniformly Elliptic Operators on Bounded Domains

We obtain Gaussian upper bounds for heat kernels of higher order differential operators with Dirichlet boundary conditions on bounded domains in $\R^N$. The bounds exhibit explicitly the nature of the spatial decay of the heat kernel close to the boundary as well as the long-time exponential decay implied by the spectral gap. We make no smoothness assumptions on our operator coefficients which we assume only to be bounded and measurable Keywords : Heat Kernel, Parabolic, Uniformly Elliptic, Gaussian.

Heat kernels of metric trees and applications

We consider the heat semi-group generated by the Laplace operator on metric trees. Among our results we show how the behavior of the associated heat kernel depends on the geometry of the tree. As applications we establish new eigenvalue estimates for Schroedinger operators on metric trees.

Critical heat kernel estimates via Hardy-Sobolev inequalities

We obtain Sobolev inequalities for the Schrodinger operator -Δ-V, where V has critical behaviour V(x)=((N-2)/2)^2|x|^{-2} near the origin. We apply these inequalities to obtain pointwise estimates on the associated heat kernel, improving upon earlier results.

曲面中曲线多边形区域上的热核

The heat kernel on curvilinear polygonal domains in surfaces

本文构造了曲面上曲线多边形区域在多种边界条件下的热核，通过热迹的短时渐近展开证明角点是谱不变量。

Asymptotics for the Heat Kernel on H-Type Groups

We give sharp asymptotic estimates at infinity of all radial partial derivatives of the heat kernel on H-type groups. As an application, we give a new proof of the discreteness of the spectrum of some natural sub-Riemannian Ornstein-Uhlenbeck operators on these groups.

Integral representation for Jacobi polynomials and application to heat kernel on quantized sphere

We derive a novel integral representations of Jacobi polynomials in terms of the Gauss hypergeometric function. Such representation is then used to give the explicit integral representation for the Heat kernel on the quantized Riemann sphere.