Related papers: Common hypercyclic vectors for composition operato…
We generalize the normalized combinatorial Laplace operator for graphs by defining two Laplace operators for hypergraphs that can be useful in the study of chemical reaction networks. We also investigate some properties of their spectra.
We study the complex symmetric structure of weighted composition--differentiation operators of order $n $ on the weighted Bergman spaces $A_{\alpha}^2$ with respect to some conjugations. Then we provide some examples of these operators.
We study composition operators on the Fock spaces $\mathcal{F}^2_\alpha(\mathbb{C}^n)$, problems considered include the essential norm, normality, spectra, cyclicity and membership in the Schatten classes. We give perfect answers for these…
The property of cyclicity of a linear operator, or equivalently the property of simplicity of its spectrum, is an important spectral characteristic that appears in many problems of functional analysis and applications to mathematical…
In this paper, we study the composition operators on an algebra of Dirichlet series, the analogue of the Wiener algebra of absolutely convergent Taylor series, which we call the Wiener-Dirichlet algebra. We study the connection between the…
In the present paper, we investigate connections between various subclasses of harmonic univalent functions by using a convolution operator involving the Pascal distribution series.
In this paper we determine a number of meaningful compositions of higher order of a set of functions, which is considered in Malesevic (1998), in implicit and explicit form. Results which are obtained are applied to the vector analysis in…
We show that families of translation operators, where the translates grow exponentially fast, do not admit common hypercyclic functions. The result is close to be optimal.
Various formulas for reciprocals of densely defined weighted composition operators in $L^2$-spaces as well as for their adjoints are provided. The relation between the reciprocal of a weighted composition operator and the product of the…
We study the composition operators on an algebra of Dirichlet series, the analogue of the Wiener algebra of absolutely convergent Taylor series, which we call the Wiener-Dirichlet algebra. The central issue is to understand the connection…
We study some basic properties of the class of universal operators on Hilbert space, and provide new examples of universal operators and universal pairs.
Enhancing a recent result of Bayart and Ruzsa we obtain a Birkhoff-type characterization of upper frequently hypercyclic operators and a corresponding Upper Frequent Hypercyclicity Criterion. As an application we characterize upper…
We introduce and study the notion of hereditary frequent hypercyclicity, which is a reinforcement of the well known concept of frequent hypercyclicity. This notion is useful for the study of the dynamical properties of direct sums of…
We generalize the notions of hypercyclic operators, $\mathfrak{U}$-frequently hypercyclic operators and frequently hypercyclic operators by introducing a new notion of hypercyclicity, called $\mathcal{A}$-frequent hypercyclicity. We then…
In this paper we investigate weighted composition operators between weak and strong vector valued weighted Bergman spaces and Hardy spaces.
We give a simple, straightforward proof of the non-hypercyclicity of an arbitrary (bounded or not) normal operator $A$ in a complex Hilbert space as well as of the collection $\left\{e^{tA}\right\}_{t\ge 0}$ of its exponentials, which,…
In this article we describe the novel method to construct fundamental solutions for operators with variable coefficients. That method was introduced in "A note on the fundamental solution for the Tricomi-type equation in the hyperbolic…
In this paper we use Nachbin's holomorphy types to generalize some recent results concerning hypercyclic convolution operators on Fr\'echet spaces of entire functions of bounded type of infinitely many complex variables.
A Cauchy type integral operator is associated to a class of integrable vector fields with complex coefficients. Properties of the integral operator are used to deduce Holder solvability of semilinear equations and a strong similarity…
In this thesis, we establish a necessary and sufficient condition for a weighted composition operator to commute with a self-adjoint weighted composition operator on the Fock space, then obtain a sufficient condition for these commuting…