相关论文: Smoothing on $L^1$ for ground state transformed se…

We study supercontractivity and hypercontractivity of Markov semigroups obtained via ground state transformation of non-local Schr\"odinger operators based on generators of symmetric jump-paring L\'evy processes with Kato-class confining…

We investigate a smoothing property for strongly-continuous operator semigroups, akin to ultracontractivity in parabolic evolution equations. Specifically, we establish the stability of this property under certain relatively bounded…

We study fractional hypoelliptic Ornstein-Uhlenbeck operators acting on $L^2(\mathbb{R}^n)$ satisfying the Kalman rank condition. We prove that the semigroups generated by these operators enjoy Gevrey regularizing effects. Two byproducts…

We investigate the concept of cylindrical Wiener process subordinated to a strictly $\alpha$-stable L\'evy process, with $\alpha\in\left(0,1\right)$, in an infinite dimensional, separable Hilbert space, and consider the related stochastic…

We establish boundedness estimates for solutions of generalized porous medium equations of the form $$ \partial_t u+(-\mathfrak{L})[u^m]=0\quad\quad\text{in $\mathbb{R}^N\times(0,T)$}, $$ where $m\geq1$ and $-\mathfrak{L}$ is a linear,…

We extend the Feynman-Kac formula for Schr\"odinger type operators on vector bundles over noncompact Riemannian manifolds to possibly very singular potentials that appear in hydrogen like quantum mechanical problems and that need not be…

We prove a new generation result in $L^1$ for a large class of non-local operators with non-degenerate local terms. This class contains the operators appearing in Fokker-Planck or Kolmogorov forward equations associated with L\'evy driven…

We study the spatial decay behaviour of resolvent kernels for a large class of non-local L\'evy operators and bound states of the corresponding Schr\"odinger operators. Our findings naturally lead us to proving results for L\'evy measures,…

This paper is to study some conditions on semigroups, generated by some class of non-densely defined operators in the closure of its domain, in order that certain bounded perturbations preserve some regularity properties of the semigroup…

We study the spatial decay of eigenfunctions of non-local Schr\"odinger operators whose kinetic terms are generators of symmetric jump-paring L\'evy processes with Kato-class potentials decaying at infinity. This class of processes has the…

We consider non-local Ornstein-Uhlenbeck (OU) operators that correspond to Ornstein-Uhlenbeck processes driven by L\'evy processes. These are ergodic Markov processes and the OU operator is in general non-normal in the $L^2$ space weighted…

We prove smoothing properties of nonlocal transition semigroups associated to a class of stochastic differential equations (SDE) driven by additive pure-jump L\'evy noise. In particular, we assume that the L\'evy process driving the SDE is…

This paper is concerned with first- and second-order optimality conditions as well as the stability for non-smooth semilinear optimal control problems involving the $L^1$-norm of the control in the cost functional. In addition to the…

We consider a simple modification of the 1D-Laplacian where non-mixed interface conditions occur at the boundaries of a finite interval. It has recently been shown that Schr\"odinger operators having this form allow a new approach to the…

We extend the theorems of [G1] on $L^p$ to $L^p_s$ Sobolev improvement for translation invariant Radon and fractional singular Radon transforms over hypersurfaces, proving $L^p$ to $L^q_s$ boundedness results for such operators. Here $q…

We consider non-local perturbations $\Delta^\psi_G$ of sub-Laplacians on a step $2$ Carnot group $G$. The perturbations are by translation-invariant non-local operators acting along the vertical directions in $G$. We use harmonic analysis…

In this paper, we establish the existence of transition density for geometric $\alpha$-stable processes by using the property of self-decomposability--a fundamental concept in the theory of L\'evy processes. In contrast to traditional and…

In this paper we apply known techniques from semigroup theory to the Schr\"odinger problem with initial conditions. To this end, we define the regularized Schr\"odinger semigroup acting on a space-time domain and show that it is strongly…

We consider Schr\"{o}dinger operators on $L^{2}({\mathbb R}^{d})\otimes L^{2}({\mathbb R}^{\ell})$ of the form $ H_{\omega}~=~H_{\perp}\otimes I_{\parallel} + I_{\perp} \otimes {H_\parallel} + V_{\omega}$, where $H_{\perp}$ and…

We study semigroups generated by general fractional Ornstein-Uhlenbeck operators acting on $L2(\mathbb R^n)$. We characterize geometrically the partial Gevrey-type smoothing properties of these semigroups and we sharply describe the blow-up…