相关论文: Heat kernels of non-symmetric jump processes: beyo…

In this paper we study the large time behavior of the (minimal) heat kernel $k_P^M(x,y,t)$ of a general time independent parabolic operator $L=u_t+P(x, \partial_x)$ which is defined on a noncompact manifold $M$. More precisely, we prove…

We study a real-valued L\'evy-type process $X$, which is locally $\alpha$-stable in the sense that its jump kernel is a combination of a `principal' (state dependent) $\alpha$-stable part with a `residual' lower order part. We show that…

We consider Dirichlet heat kernel $p_a^{(\mu)}(t,x,y)$ for the Bessel differential operator $L^{(\mu)}=\frac{d^2}{dx^2}+\frac{2\mu+1}{2x}$, $\mu\in\mathbb{R}$, in half-line $(a,\infty)$, $a>0$, and provide its asymptotic expansions for…

Kernels of $\alpha$-permanental processes of the form \[ v(x,y)=u(x,y)+f(y),\qquad x,y\in S, \] in which $u(x,y)$ is symmetric, and $f$ is an excessive function for the Borel right process with potential densities $u(x,y)$, are considered.…

We investigate densities of vaguely continuous convolution semigroups of probability measures on $\mathbb{R}^d$. We expose that many typical conditions on the characteristic exponent repeatedly used in the literature of the subject are…

We establish sharp upper and lower bounds of Gaussian type for the heat kernel in the metric measure space satisfying $\RCD(0,N)$ ( equivalently, $\RCD^\ast(0,N)$) condition with $N\in \mathbb{N}\setminus\{1\}$ and having maximum volume…

We construct and estimate the fundamental solution of highly anisotropic space-inhomogeneous integro-differential operators. We use the Levi method. We give applications to the Cauchy problem for such operators.

I discuss the trace of a heat kernel Tr[e^(-tA)] for compact fuzzy spaces. In continuum theory its asymptotic expansion for t -> +0 provides geometric quantities, and therefore may be used to extract effective geometric quantities for fuzzy…

The formulation of gauge theories on compact Riemannian manifolds with boundary leads to partial differential operators with Gilkey--Smith boundary conditions, whose peculiar property is the occurrence of both normal and tangential…

In this paper, first we consider the uniform complex time heat kernel estimates of $e^{-z(-\Delta)^{\frac{\alpha}{2}}}$ for $\alpha>0, z\in \mathbb{C}^+$. When $\frac{\alpha}{2}$ is not an integer, generally the heat kernel doest not have…

Let $L$ be a closed, densely defined operator of type $ \omega $ on $ L^2(\mathbb{R}^n)$ with $0 \leq \omega < \pi/2 $. We assume that $ L $ possesses a bounded $ H_\infty $-functional calculus and that its heat kernel satisfies suitable…

We consider the null-controllability of a non-local heat equation by interior $L^2(\Omega)$ controls. We confirm a conjecture of Lissy and Zuazua by showing that it is enough to assume that the kernel $k(x,\xi)$ is symmetric and…

Let $M$ be a complete non-compact manifold satisfying the volume doubling condition, with doubling index $N$ and reverse doubling index $n$, $n\le N$, both for large balls. Assume a Gaussian upper bound for the heat kernel, and an…

Let $\mathbf{X}=\{X_t\}_{t\geq 0}$ be a L\'evy process in $\mathbb{R}^d$ and $\Omega$ be an open subset of $\mathbb{R}^d$ with finite Lebesgue measure. In this article we consider the quantity $H (t) = \int_{\Omega}\mathbb{P}_{x} (X_t\in…

The heat kernel expansion is a very convenient tool for studying one-loop divergences, anomalies and various asymptotics of the effective action. The aim of this report is to collect useful information on the heat kernel coefficients…

We consider the elliptic system of linear elasticity with bounded measurable coefficients in a domain where the second Korn inequality holds. We construct heat kernel of the system subject to Dirichlet, Neumann, or mixed boundary condition…

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…

We describe the small-time heat kernel asymptotics of real powers $\Delta^r$, $r \in (0,1)$ of a non-negative self-adjoint generalized Laplacian $\Delta$ acting on the sections of a hermitian vector bundle $\mathcal E$ over a closed…

We analyze the spectra of general non-minimal second-order operators. To do this, we derive the local part of the trace of the second Seeley-DeWitt heat kernel coefficient for such operators in a completely model-independent way.…

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…