Related papers: On the non-local heat kernel expansion

Let $\Delta$ be the Laplace--Beltrami operator acting on a non-doubling manifold with two ends $\mathbb R^m \sharp \mathcal R^n$ with $m > n \ge 3$. Let $\frak{h}_t(x,y)$ be the kernels of the semigroup $e^{-t\Delta}$ generated by $\Delta$.…

Auscher, McIntosh and Tchamitchian studied the heat kernels of second order elliptic operators in divergence form with complex bounded measurable coefficients on $\mathbb{R}^n$. In particular, in the case when $n=2$ they obtained Gaussian…

We introduce a theory of local kernels, which generalize the kernels used in the standard diffusion maps construction of nonparametric modeling. We prove that evaluating a local kernel on a data set gives a discrete representation of the…

We consider a generic curved non-commutative torus extending the notion of conformally deformed non-commutative torus from \cite{Connes-Tretkoff}. In general, a curved non-commutative torus is no longer represented by a spectral triple, not…

Being motivated by physical applications (as the phi^4 model) we calculate the heat kernel coefficients for generalised Laplacians on the Moyal plane containing both left and right multiplications. We found both star-local and star-nonlocal…

In this note I present some properties of sub-Laplaceans associated with a collection of smooth vector fields satisfying H\"ormander's finite rank assumption. One notable aspect of the paper is the development of the fractional powers of…

We extend the uncertainty principle, the Cowling--Price theorem, on non-compact Riemannian symmetric spaces $X$. We establish a characterization of the heat kernel of the Laplace--Beltrami operator on $X$ from integral estimates of the…

In this paper we discuss non-local operators with killing potentials, which may not be in the standard Kato class. We first discuss factorization of their Dirichlet heat kernels in metric measure spaces. Then we establish explicit estimates…

We review the status of covariant methods in quantum field theory and quantum gravity, in particular, some recent progress in the calculation of the effective action via the heat kernel method. We study the heat kernel associated with an…

Computer algebra methods are applied to investigation of spectral asymptotics of elliptic differential operators on curved manifolds with torsion and in the presence of a gauge field. In this paper we present complete expressions for the…

In this paper we give Hamilton's Laplacian estimates for the heat equation on complete noncompact manifolds with nonnegative Ricci curvature. As an application, combining Li-Yau's lower and upper bounds of the heat kernel, we give an…

We consider a class of constant-coefficient partial differential operators on a finite-dimensional real vector space which exhibit a natural dilation invariance. Typically, these operators are anisotropic, allowing for different degrees in…

In this paper, we generally expressed the virial expansion of ideal quantum gases by the heat kernel coefficients for the corresponding Laplace type operator. As examples, we give the virial coefficients for quantum gases in $d$-dimensional…

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…

A general class of heat operators over non-archimedean local fields acting on $L_2$-function spaces on affinoid domains in the local field are developed. $L_2$-spaces and integral operators invariant under the action of a non-archimedean…

We suggest a new technique of the asymptotic heat kernel expansion for minimal higher derivative operators of a generic $2M$-th order, $F(\nabla)=(-\Box)^M+\cdots$, in the background field formalism of gauge theories and quantum gravity.…

In the sub-Riemannian manifolds, on the one hand, following Baudoin-Garofalo \cite{BaudoinGarofalo}, the upper bound for heat kernels associated to a class of locally subelliptic operators are given under the generalized curvature-dimension…

Classical and non classical Besov and Triebel-Lizorkin spaces with complete range of indices are developed in the general setting of Dirichlet space with a doubling measure and local scale-invariant Poincar\'e inequality. This leads to Heat…

We give optimal bounds for the radial, space and time derivatives of arbitrary order of the heat kernel of the Laplace--Beltrami operator on Damek--Ricci spaces. In the case of symmetric spaces of rank one, these complete and actually…

In this note we establish the large time non-negativity of the heat kernel for a class of elliptic differential operators on closed, Riemannian manifolds, and apply this result to a problem from conformal differential geometry.