Related papers: Asymptotics for the Heat Kernel on H-Type Groups

We study integral kernels of strongly continuous semigroups on Lebesgue spaces over metric measure spaces. Based on semigroup smoothing properties and abstract Morrey-type inequalities, we give sufficient conditions for H\"older or…

We investigate a Riemann-Hilbert problem (RHP), whose solution corresponds to a group of $q$-orthogonal polynomials studied earlier by Ismail et al. Using RHP theory we determine new asymptotic results in the limit as the degree of the…

Upper and lower bounds on the heat kernel on complete Riemannian manifolds were obtained in a series of pioneering works due to Cheng-Li-Yau, Cheeger-Yau and Li-Yau. However, these estimates do not give a complete picture of the heat kernel…

We prove sharp two-sided global estimates for the heat kernel associated with a Euclidean sphere of arbitrary dimension. This solves a long-standing open problem.

The goal of this article is twofold: in a first part, we prove Gaussian estimates for the heat kernel of Schr{\"o}dinger operators delta + V whose potential V is "small at infinity" in an integral sense. In a second part, we prove sharp…

The high temperature asymptotics of the Helmholtz free energy of electromagnetic field subjected to boundary conditions with spherical and cylindrical symmetries are constructed by making use of a general expansion in terms of heat kernel…

In this paper, we study the heat kernel associated to the intrinsic sublaplacian on a quaternionic contact manifold considered as a subriemannian manifold. More precisely, we explicitly compute the first two coefficients $c_0$ and $c_1$…

We study the heat semigroup generated by two-dimensional Schroedinger operators with compactly supported magnetic field. We show that if the field is radial, then the large time behavior of the associated heat kernel is determined by its…

Let $(X,d)$ be a proper ultrametric space. Given a measure $m$ on $X$ and a function $B \mapsto C(B)$ defined on the collection of all non-singleton balls $B$ of $X$, we consider the associated hierarchical Laplacian $L=L_{C}\,$. The…

This is first of series papers on new two-side Gaussian bounds for the heat kernel $H(x,y,t)$ on a complete manifold $(M,g)$. In this paper, on a complete manifold $M$ with $Ric(M)\geq 0$, we obtain new two-side Gaussian bounds for the heat…

We perform quantitative spectral analysis of the self-adjoint Dirichlet Laplacian $\mathsf{H}$ on an unbounded, radially symmetric (generalized) parabolic layer $\mathcal{P}\subset\mathbb{R}^3$. It was known before that $\mathsf{H}$ has an…

This paper presents a closed-form expression for the integral kernels associated with the derivatives of the Ornstein-Uhlenbeck semigroup $e^{tL}$. Our approach is to expand the Mehler kernel into Hermite polynomials and applying the powers…

We establish dimension-independent estimates related to heat operators e^{tL} on manifolds. We first develop a very general contractivity result for Markov kernels which can be applied to diffusion semigroups. Second, we develop estimates…

Using time dependent Lyapunov functions, we prove pointwise upper bounds for the heat kernels of some nonautonomous Kolmogorov operators with possibly unbounded drift and diffusion coefficients.

We prove that on an asymptotically Euclidean boundary groupoid, the heat kernel of the Laplacian is a smooth groupoid pseudo-differential operator.

In this note, we look at some hypoelliptic operators arising from nilpotent rank 2 Lie algebras. In particular, we concentrate on the diffusion generated by three Brownian motions and their three L\'evy areas, which is the simplest…

We give large-time asymptotic estimates, both in uniform and $L^1$ norms, for solutions of the Dirichlet heat equation in the complement of a bounded open set of $\mathbb{R}^d$ satisfying certain technical assumptions. We always assume that…

For $d\geq 2$, we establish the existence and uniqueness of heat kernels for a large class of time-dependent second order diffusion operator with jumps, which is the sum of time-dependent of a second order elliptic differential operators…

We study new heat kernel estimates for the Neumann heat kernel on a compact manifold with positive Ricci curvature and convex boundary. As a consequence, we obtain new lower bounds for the Neumann eigenvalues which are consistent with…

In this note we show the optimal gradient estimate for heat kernels of stable-like operators by providing a counterexample.