Related papers: A Note on Weak Hypercyclicity and Linear Fractiona…
In this paper, we pursue our series of papers aiming to show the applicability of the concept of very weak solutions. We consider a wave model with irregular position dependent mass and dissipation terms, in particular, allowing for…
In Phys. Rev. Lett. 113, 120404 (2014) [arXiv:1403.2362], Ferrie and Combes claim that weak values could be a statistical artifact caused by correlations between the disturbance and the post-selection condition imposed on the output. In…
The weak equivalence principle is studied in a space with noncommutativity of coordinates and noncommutativity of momenta. We find conditions on the parameters of noncommutativity which give the possibility to recover the equivalence…
Interfaces play a central role in determining compatible component compositions by prescribing permissible interactions between a service provider (server) and its consumers (clients). The high degree of concurrency in asynchronous…
We generalize a result for the translation $C_0$-semigroup on $L^p(\R_+,\mu)$ about the equivalence of being chaotic and satisfying the Frequent Hypercyclicity criterion due to Mangino and Peris to certain weighted composition…
Let $T$ be a so-called operator of Read's type on a (real or complex) separable Banach space, having no non-trivial invariant subset. We prove in this note that $T\oplus T$ is then hypercyclic, i.e. that $T$ satisfies the Hypercyclicity…
We investigate four key issues with using a nonzero weak value of the spatial projection operator to infer the past path of an individual quantum particle. First, we note that weak measurements disturb a system, so any approach relying on…
We study properties of the following four classes of operators on the Fock space in $\mathbb C^n:$ 1) weakly localized operators; 2) sufficiently localized operators in the sense of Xia and Zheng; 3) sufficiently localized operators; 4)…
The operator of weak commutativity between isomorphic groups $H$ and $H^{\psi }$ was defined by Sidki as \begin{equation*} \chi (H)=\left\langle H\,H^{\psi }\mid \lbrack h,h^{\psi }]=1\,\forall \,h\in H\right\rangle \text{.}…
We consider radial tree extensions of one-dimensional quasi-periodic Schroedinger operators and establish the stability of their absolutely continuous spectra under weak but extensive perturbations by a random potential. The sufficiency…
We introduce a notion of weak convergence in arbitrary metric spaces. Metric functionals are key in our analysis: weak convergence of sequences in a given metric space is tested against all the metric functionals defined on said space. When…
Reversible systems feature both forward computations and backward computations, where the latter undo the effects of the former in a causally consistent manner. The compositionality properties and equational characterizations of strong and…
A tuple $(T_1,\dots,T_n)$ of continuous linear operators on a topological vector space $X$ is called hypercyclic if there is $x\in X$ such that the the orbit of $x$ under the action of the semigroup generated by $T_1,\dots,T_n$ is dense in…
We study interacting components and their compatibility with respect to synchronous and asynchronous composition. The behavior of components is formalized by I/O-transition systems. Synchronous composition is based on simultaneous execution…
In this paper we give some sufficient conditions of analyticity and univalence for functions defined by an integral operator. Next, we refine the result to a quasiconformal extension criterion with the help of the Becker's method. Further,…
We give a sufficient condition for a composition operator with positive characteristic to be compact on the Hardy space of Dirichlet series.
Weak value is increasingly acknowledged as an important research tool for probing quantum pre- and post-selected ensembles, where some extraordinary phenomena occur. We generalize this concept to the broader notion of "weak potential" which…
In this paper, we characterize supercyclic weighted composition operators on a large class of solid Banach function spaces, in particular on Lebesgue, Orlicz and Morrey spaces. Also, we characterize supercyclic weighted composition…
We study frequent hypercyclicity in the context of strongly continuous semigroups of operators. More precisely, we give a criterion (sufficient condition) for a semigroup to be frequently hypercyclic, whose formulation depends on the Pettis…
We demonstrate that being a hyperbolicity preserver does not imply monotonicity for infinite order differential operators on $\mathbb{R}[x]$, thereby settling a recent conjecture in the negative. We also give some sufficient conditions for…