相关论文: Compactness of semigroups generated by symmetric n…

We present conservativeness criteria for sub-Markovian semigroups generated by divergence type operators with specified infinitesimally invariant measures. The conservativeness criteria in this article are derived by $L^1$-uniqueness and…

We define a suitable class $\mathcal{PDG}$ of functions bearing unbalanced energy estimates, that are embodied by local weak subsolutions to doubly nonlinear, double-phase, Orlicz-type and fully anisotropic operators. Yet we prove that…

A function $f\in \BUC(\R^d)$ is said to be weakly* almost periodic, denoted $f\in\APs(\R^d)$, if there is $g\in\AP(\R^d)$, such that, $\oM(|f-g|)=0$, where $\BUC(\R^d)$ and $\AP(\R^d)$ are, respectively, the space of bounded uniformly…

In this article we study perturbations of local, nonlinear Dirichlet forms on arbitrary topological measure spaces. We show that the semigroup of a local Dirichlet form \(\mathcal{E}\) dominates the semigroup generated by another functional…

In this note, we establish $L^p$-bounds for the semigroup $e^{-tq^w(x,D)}$, $t \ge 0$, generated by a quadratic differential operator $q^w(x,D)$ on $\mathbb{R}^n$ that is the Weyl quantization of a complex-valued quadratic form $q$ defined…

Let $(M,\textit{g},\sigma)$ be an $m$-dimensional closed spin manifold, with a fixed Riemannian metric $\textit{g}$ and a fixed spin structure $\sigma$; let $\mathbb{S}(M)$ be the spinor bundle over $M$. The spinorial Yamabe-type problems…

Let ${\sf G}$ be a locally compact group with polynomial growth of order $d$, a polynomial weight $\nu$ on ${\sf G}$ and a Fell bundle $\mathscr C\overset{q}{\to}{\sf G}$. We study the Banach $^*$-algebras $L^1({\sf G}\,\vert\,\mathscr C)$…

Given two measurable functions $V(r)\geq 0$ and $K(r)> 0$, $r>0$, we define the weighted spaces \[ H_V^1 = \{u \in D^{1,2}(\mathbb{R}^N): \int_{\mathbb{R}^N}V(|x|)u^{2}dx < \infty \}, \quad L_K^q = L^q(\mathbb{R}^N,K(|x|)dx) \] and study…

Let $U:[0,\infty)^2 \to [0,\infty)$ be a~measurable kernel satisfying: (i) $U(x,y)$ is nonincreasing in $x$ and nondecreasing in $y$; (ii) there exists a~constant $\theta>0$ such that $U(x,z) \le \theta\left( U(x,y)+U(y,z) \right)$ for all…

For each countable residually finite group $G$, we present examples of irregular Toeplitz subshifts in $\{0,1\}^G$ that are topo-isomorphic extensions of its maximal equicontinuous factor. To achieve this, we first establish sufficient…

In this paper, the object of our investigation is the following Littlewood-Paley square function $g$ associated with the Schr\"odinger operator $L=-\Delta +V$ which is defined by:…

We study sequences of nonlocal quadratic forms and function spaces that are related to Markov jump processes in bounded domains with a Lipschitz boundary. Our aim is to show the convergence of these forms to local quadratic forms of…

Let $m(G)$ be the infimum of the volumes of all open subgroups of a unimodular locally compact group $G$. Suppose integrable functions $\phi_1 , \phi_2 \colon G \to [0,1]$ satisfy $\| \phi_1 \| \leq \| \phi_2 \|$ and $\| \phi_1 \| + \|…

Every topological group $G$ has some natural compactifications which can be a useful tool of studying $G$. We discuss the following constructions: (1) the greatest ambit $S(G)$ is the compactification corresponding to the algebra of all…

In this paper, we investigate spectral properties of explosive symmetric Markov processes. Under a condition on its life time, we prove the $L^1$-semigroup of Markov processes become compact operators.

If $({\cal E}, {\cal D})$ is a symmetric, regular, strongly local Dirichlet form on $L^2 (X,m)$, admitting a carr\'{e} du champ operator $\Gamma$, and $p>1$ is a real number, then one can define a nonlinear form ${\cal E}^p$ by the formula…

We introduce the {\it Ellis semigroup} of a nonautonomous discrete dynamical system $(X,f_{1,\infty})$ when $X$ is a metric compact space. The underlying set of this semigroup is the pointwise closure of $\{f\sp{n}_1 \, |\, n\in…

This paper is concerned with a class of singular stable-like Dirichlet forms on $\R^d$, which are generated by $d$ independent copies of a one-dimensional symmetric $\alpha$-stable process, and whose L\'evy jump kernel measure is…

We remove the local boundedness for $\mathscr{E}_{\alpha}$-subharmonicity in the framework of (not necessarily strongly local) regular symmetric Dirichlet form $(\mathscr{E},D(\mathscr{E}))$ with $\alpha\geq0$ and establish the stochastic…

We put together a general framework to deal with elliptic and parabolic equations associated with (nonlinear) nonlocal (fractional order) operators. Many well-known nonlocal operators enter into our framework, and in addition one may…