Related papers: Large time behavior of the heat kernel

The asymptotic expansion of the heat-kernel for small values of its argument has been studied in many different cases and has been applied to 1-loop calculations in Quantum Field Theory. In this thesis we consider this asymptotic behavior…

We investigate heat kernel estimates of the form $p_{t}(x, x)\geq c_{x}t^{-\alpha},$ for large enough $t,$ where $\alpha$ and $c_{x}$ are positive reals and $c_{x}$ may depend on $x,$ on manifolds having at least one end.

We give a short overview of the effective action approach in quantum field theory and quantum gravity and describe various methods for calculation of the asymptotic expansion of the heat kernel for second-order elliptic partial differential…

We consider a self-adjoint non-negative operator $H$ in a Hilbert space $\mathsf{L}^2(X,{\rm d}\mu)$. We assume that the semigroup $(\mathrm{e}^{-t H})_{t>0}$ is defined by an integral kernel, $p$, which allows an estimate of the form…

We prove heat kernel estimates for the $\bar\partial$-Neumann Laplacian acting in spaces of differential forms over noncompact, strongly pseudoconvex complex manifolds with a Lie group symmetry and compact quotient. We also relate our…

We study the heat kernel for a Laplace type partial differential operator acting on smooth sections of a complex vector bundle with the structure group $G\times U(1)$ over a Riemannian manifold $M$ without boundary. The total connection on…

For a given bounded domain $\Omega$ with smooth boundary in a smooth Riemannian manifold $(\mathcal{M},g)$, we establish a procedure to get all the coefficients of the asymptotic expansion of the trace of the heat kernel associated with the…

By using ideas and strong results borrowed from the classical moment problem, we show how -under very general conditions- a discrete number of values of the spectral zeta function (associated generically with a non-decreasing sequence of…

We consider second-order elliptic partial differential operators acting on sections of vector bundles over a compact Riemannian manifold without boundary, working without the assumption of Laplace-like principal part $-\N^\mu\N_\mu$. Our…

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…

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 $\Delta$.…

In this paper we establish the existence and uniqueness of heat kernels to a large class of time-inhomogenous non-symmetric nonlocal operators with Dini's continuous kernels. Moreover, quantitative estimates including two-sided estimates,…

We study strong ratio limit properties and the exact long time asymptotics of the heat kernel of a general second-order parabolic operator which is defined on a noncompact Riemannian manifold.

We study the asymptotic behaviour of solutions of a class of linear non-local measure-valued differential equations with time delay. Our main result states that the solutions asymptotically exhibit a parabolic like behaviour in the large…

The purpose of this article is to establish upper and lower estimates for the integral kernel of the semigroup exp(-tP) associated to a classical, strongly elliptic pseudodifferential operator P of positive order on a closed manifold. The…

We obtain two-sided estimates for the heat kernel (or the fundamental function) associated with the following fractional Schr\"odinger operator with negative Hardy potential $$\Delta^{\alpha/2} -\lambda |x|^{-\alpha}$$ on $\RR^d$, where…

Given any $d$-dimensional Lipschitz Riemannian manifold $(M,g)$ with heat kernel $\mathsf{p}$, we establish uniform upper bounds on $\mathsf{p}$ which can always be decoupled in space and time. More precisely, we prove the existence of a…

This paper studies by means of standard analytic tools the small time behavior of the heat content over a bounded Lebesgue measurable set of finite perimeter by working with the set covariance function and by imposing conditions on the heat…

We approximate the heat kernel $h(x,y,t)$ on a compact connected Riemannian manifold $M$ without boundary uniformly in $(x,y,t)\in M\times M\times [a,b]$, $a>0$, by $n$-fold integrals over $M^n$ of the densities of Brownian bridges.…

When studying non-symmetric nonlocal operators $$ {\cal L} f(x) = \int_{{\bf R}^d} \left( f(x+z)-f(x)-\nabla f(x)\cdot z 1_{\{|z|\leq 1\}} \right) \frac{\kappa (x, z)}{|z|^{d+\alpha}} d z , $$ where $0<\alpha<2$ and $\kappa (x, z)$ is a…