Related papers: Unbounded Chaotic Weighted Pseudo-shift

We study cusped Wilson line operators in the Abelian Higgs model in $ d = 4 - \epsilon $ at large external charges. Using a double-scaling limit $ Q \to \infty $, $ \epsilon \to 0 $ with $ Q\epsilon $ fixed, we develop a semiclassical…

We give sufficient conditions on an asymptotic $\ell_p$ (for $1 < p < \infty$) Banach space which ensure the space admits an operator which is not a compact perturbation of a multiple of the identity. These conditions imply the existence of…

In this paper, we study hyponormal weighed composition operators on the Hardy and weighted Bergman spaces. For functions $\psi \in A(\mathbb{D})$ which are not the zero function, we characterize all hyponormal compact weighted composition…

We consider a nonlinear oscillator with fractional derivative of the order alpha. Perturbed by a periodic force, the system exhibits chaotic motion called fractional chaotic attractor (FCA). The FCA is compared to the ``regular'' chaotic…

Let $u$ be a holomorphic function and $\varphi$ a holomorphic self-map of the open unit disk $\mathbb{D}$ in the complex plane. We give some new characterizations for the boundedness of the weighted composition operators $uC_{\varphi}$ from…

We give a sufficient condition for two operators to be disjointly frequently hypercyclic. We apply this criterion to composition operators acting on $H(\mathbb D)$ or on the Hardy space $H^2(\mathbb D)$. We simplify a result on disjoint…

We study unitarily equivalent bilateral weighted shifts with operator weights. We establish a general characterization of unitary equivalence of such shifts under the assumption that the weights are quasi-invertible. We prove that under…

We provide a sufficient condition for an operator $T$ on a non-metrizable and sequentially separable topological vector space $X$ to be sequentially hypercyclic. This condition is applied to some particular examples, namely, a composition…

In this paper we study the chaotic behaviour of the heat semigroup generated by the Dunkl-Laplacian on weighted $ L^p$ spaces. In the case of the heat semigroup associated to the standard Laplacian we obtain a complete picture on the spaces…

According to Kim, Peris and Song, a continuous linear operator $T$ on a complex Banach space $X$ is called {\it numerically hypercyclic} if the numerical orbit $\{f(T^nx):n\in\N\}$ is dense in $\C$ for some $x\in X$ and $f\in X^*$…

We give a simple characterization of chaos for weighted composition $C_0$-semigroups on $L^p_\rho(\Omega)$ for an open interval $\Omega\subseteq\mathbb{R}$. Moreover, we characterize chaos for these classes of $C_0$-semigroups on the closed…

We first consider some questions raised by N. Zorboska in her thesis. In particular she asked for which sequences $\beta$ every symbol $\varphi \colon \mathbb{D} \to \mathbb{D}$ with $\varphi \in H^2 (\beta)$ induces a bounded composition…

We study a modified Kac model where the classical kinetic energy is replaced by an arbitrary energy function $\phi(v)$, $v \in \mathbb{R}$. The aim of this paper is to show that the uniform density with respect to the microcanonical measure…

In this paper, we explore the construction and dynamical properties of $\mathcal{S}$-limited shifts. An $S$-limited shift is a subshift defined on a finite alphabet $\mathcal{A} = \{1, \ldots,p\}$ by a set $\mathcal{S} = \{S_1, \ldots,…

We show that linear chaos in the space $c(\mathbb{N})$ of convergent sequences cannot be arrived at by merely extending the weighted backward shifts in the space $c_0(\mathbb{N})$ of vanishing sequences. Applying a newly found sufficient…

Let $\phi(z)=(\phi_1(z),...,\phi_n(z))$ be a holomorphic self-map of $B_n$ and $\psi(z)$ a holomorphic function on $B_n$, and $H(B_n)$ the class of all holomorphic functions on $B_n$, where $B_n$ is the unit ball of $C^n$, the weight…

A new method of verifying the subnormality of unbounded Hilbert space operators based on an approximation technique is proposed. Diverse sufficient conditions for subnormality of unbounded weighted shifts on directed trees are established.…

We consider divergence form operators with complex coefficients on an open subset of Euclidean space. Boundary conditions in the corresponding parabolic problem are dynamical, that is, the time derivative appears on the boundary. As a…

In this paper, some sub-classes of paranormal weighted conditional expectation type operators, such as *-paranormal, quasi-*-paranormal and (n; k)-quasi-*-paranormal weighted conditional expectation type opera- tors on $L^2(\Sigma)$ are…

On a manifold $X$ with boundary and bounded geometry we consider a strongly elliptic second order operator $A$ together with a degenerate boundary operator $T$ of the form $T=\varphi_0\gamma_0 + \varphi_1\gamma_1$. Here $\gamma_0$ and…