Related papers: Heat kernels, symplectic geometry, moduli spaces a…
Heat kernel expansion coefficients are calculated for vacuum fluctuations with distributional background potentials and field strengths. Terms up to and including t^5/2 are presented.
We study the heat kernel asymptotics for the Laplace type differential operators on vector bundles over Riemannian manifolds. In particular this includes the case of the Laplacians acting on differential p-forms. We extend our results…
We study the heat kernel transform on a nilmanifold M associated to a H-type group. Using a reduction technique we reduce the problem to the case of Heisenberg groups. The image of $ L^2(M) $ under the heat kernel transform is shown to be a…
We study semigroups generated by two-dimensional relativistic Hamiltonians with magnetic field. In particular, for compactly supported radial magnetic field we show how the long time behaviour of the associated heat kernel depends on the…
This paper presents a detailed analysis of the heat kernel on an $(\mathbb{N}\times\mathbb{N})$-parameter family of compact metric measure spaces, which do not satisfy the volume doubling property. In particular, uniform bounds of the heat…
We present a brief overview of several approaches for calculating the local asymptotic expansion of the heat kernel for Laplace-type operators. The different methods developed in the papers of both authors some time ago are described in…
This paper aims to study the asymptotic behaviour of the fundamental solutions (heat kernels) of non-local (partial and pseudo differential) equations with fractional operators in time and space. In particular, we obtain exact asymptotic…
In this paper we extend a gradient estimate of R. Hamilton for positive solutions to the heat equation on closed manifolds to bounded positive solutions on complete, non-compact manifolds with $Rc \geq -Kg$. We accomplish this extension via…
We consider heat kernels on Weyl chambers corresponding to Laplacians subject to mixed Dirichlet-Neumann boundary conditions imposed on the boundary. Using purely analytic tools we prove genuinely sharp two-sided global estimates in the…
Under the assumption of positive multiplicity, we obtain basic estimates of the hypergeometric functions F\_\la and G\_\la of Heckman and Opdam, and sharp estimates of the particular functions F\_0 and G\_0. Next we prove the Paley-Wiener…
In this paper we study the symplectic and Poisson geometry of moduli spaces of flat connections over quilted surfaces. These are surfaces where the structure group varies from region to region in the surface, and where a reduction (or…
We establish a new formula for the heat kernel on regular trees in terms of classical I-Bessel functions. Although the formula is explicit, and a proof is given through direct computation, we also provide a conceptual viewpoint using the…
Given a class of closed Riemannian manifolds with prescribed geometric conditions, we introduce an embedding of the manifolds into $\ell^2$ based on the heat kernel of the Connection Laplacian associated with the Levi-Civita connection on…
The universality properties of kernels characterize the class of functions that can be approximated in the associated reproducing kernel Hilbert space and are of fundamental importance in the theoretical underpinning of kernel methods in…
In this paper, we study Ornstein-Uhlenbeck operators with quadratic potentials. We use Hamiltonian formalism to characterise the singularities produced by the potentials by finding explicit geodesics of the operators, and obtain the heat…
We propose the multiple reflection expansion as a tool for the calculation of heat kernel coefficients. As an example, we give the coefficients for a sphere as a finite sum over reflections, obtaining as a byproduct a relation between the…
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 introduce a class of non-commutative Heisenberg like infinite dimensional Lie groups based on an abstract Wiener space. The Ricci curvature tensor for these groups is computed and shown to be bounded. Brownian motion and the…
We study orbital functions associated to Kleinian groups through the heat kernel approach developed in \cite{artmoiheatcounting1}.
We use the heat kernel (on differential forms) on a compact Riemannian manifold to assign a real number to a k-tuple of cycles on the manifold satisfying certain conditions. If k is 2, this number is the ordinary topological linking number,…