Related papers: Dirichlet heat kernel estimates for rectilinear st…
Let $(M, g)$ be a smooth n-dimensional Riemannian manifold for $n\ge 2$. Consider the conformal perturbation $\tilde{g}=h g$ where $h$ is a smooth bounded positive function on $M$. Denote by $\tilde{p}_t(x,y)$ the heat kernel of manifolds…
The heat trace of a planar polygon contains corner terms depending only on the opening angles, while the heat trace of a smooth planar domain contains curvature terms along the boundary. We show that, for curvilinear polygons, these two…
Let $L$ be an elliptic differential operator on a complete connected Riemannian manifold $M$ such that the associated heat kernel has two-sided Gaussian bounds as well as a Gaussian type gradient estimate. Let $L^{(\aa)}$ be the…
Wavelet bases and frames consisting of band limited functions of nearly exponential localization on Rd are a powerful tool in harmonic analysis by making various spaces of functions and distributions more accessible for study and…
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…
We give matching upper and lower bounds for the Dirichlet heat kernel of a Schr\"odinger operator $\Delta+W$ in the domain above the graph of a bounded Lipschitz function, in the case when $W$ decays away from the boundary faster than…
The present paper continues the study of infinite dimensional calculus via regularization, started by C. Di Girolami and the second named author, introducing the notion of weak Dirichlet process in this context. Such a process X, taking…
We give local in time sharp two sided estimates of the heat kernel associated with the relativistic stable operator perturbed by a critical (Hardy) potential.
We study positive definiteness of kernels $K(x,y)$ on two-point homogeneous spaces. As opposed to the classical case, which has been developed and studied in the existing literature, we allow the kernel to have an (integrable) singularity…
We investigate dilaton-gravity models whose solutions contain a large portion of the static patch of dS$_2$. The thermodynamic properties of these theories are considered both in the presence of a finite Dirichlet wall, as well as for…
For a planar domain $\Omega$, we consider the Dirichlet spaces with respect to a base point $\zeta\in\Omega$ and the corresponding kernel functions. It is not known how these kernel functions behave as we vary the base point. In this note,…
In this paper we continue our investigation of the potential theory of Markov processes with jump kernels decaying at the boundary. To be more precise, we consider processes in ${\mathbb R}^d_+$ with jump kernels of the form ${\mathcal…
Suppose that $d\geq1$ and $\alpha\in (1, 2)$. Let $Y$ be a rotationally symmetric $\alpha$-stable process on $\R^d$ and $b$ a $\R^d$-valued measurable function on $\R^d$ belonging to a certain Kato class of $Y$. We show that $\rd X^b_t=\rd…
We study qualitative properties of initial traces of nonnegative solutions to a semilinear heat equation in a smooth domain under the Dirichlet boundary condition. Furthermore, for the corresponding Cauchy--Dirichlet problem, we obtain…
This paper studies strongly local symmetric Dirichlet forms on general measure spaces. The underlying space is equipped with the intrinsic metric induced by the Dirichlet form, with respect to which the metric measure space does not…
We study absolute-continuity properties of a class of stochastic processes, including the gamma and the Dirichlet processes. We prove that the laws of a general class of non-linear transformations of such processes are locally equivalent to…
This paper investigates the theoretical properties of Dirichlet kernel density estimators for compositional data supported on simplices, for the first time addressing scenarios involving time-dependent observations characterized by strong…
The paper introduces new sufficient conditions of strict positive definiteness for kernels on d-dimensional spheres which are not radially symmetric but possess specific coefficient structures. The results use the series expansion of the…
In this paper, we focus on the heat kernel estimates for diffusions and jump processes on metric measure spaces satisfying a weak chain condition, where the length of a nearly shortest $\varepsilon$-chain between two points $x,y$ is…
We establish sharp pointwise estimates for the ground states of some singular fractional Schr\"odinger operators on relatively compact Euclidean subsets. The considered operators are of the type $(-\Delta)^{\alpha/2}|_\Om-c|x|^{-\alpha}$,…