Related papers: Inverse of $\mathcal{U}$-frequently hypercyclic op…

Explicit inversion formulas for a subclass of integral operators with $D$-difference kernels on a finite interval are obtained. A case of the positive operators is treated in greater detail. An application to the inverse problem to recover…

Consider the set of unitary operators on a complex separable Hilbert space $\hilh$, denoted as $\mathcal{U}(\hilh)$. Consider $1<p<\infty$. We establish that a function $f$ defined on the unit circle $\cir$ is $n$ times continuously…

Motivated by a recent investigation of Costakis et al. on the notion of recurrence in linear dynamics, we study various stronger forms of recurrence for linear operators, in particular that of frequent recurrence. We study, among other…

In this note we consider a certain class of convolution operators acting on the L_p spaces of the one dimensional torus. We prove that the identity minus such an operator is nicely invertible on the subspace of functions with mean zero.

We show that every hypercyclic operator on a real locally convex space admits a dense, invariant linear manifold of hypercyclic vectors.

Let $I$ be a countably infinite index set, and let $X$ be a Banach sequence space over $I.$ In this article, we characterize disjoint hypercyclic and supercyclic weighted pseudo-shift operators on $X$ in terms of the weights, the OP-basis,…

A unitary operator $V$ and a rank $2$ operator $R$ acting on a Hilbert space $\H$ are constructed such that $V+R$ is hypercyclic. This answers affirmatively a question of Salas whether a finite rank perturbation of a hyponormal operator can…

We study hypercyclicity properties of a family of non-convolution operators defined on spaces of holomorphic functions on $\mathbb{C}^N$. These operators are a composition of a differentiation operator and an affine composition operator,…

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…

In this paper we study operators of the form $M(\phi)=T(\phi)+H(\phi)$ where $T(\phi)$ and $H(\phi)$ are the Toeplitz and Hankel operators acting on $H^p(\T)$ with generating function $\phi\in L^\iy(\T)$. It turns out that $M(\phi)$ is…

A bounded linear operator T on Hilbert space is subspace-hypercyclic for a subspace M if there exists a vector whose orbit under T intersects the subspace in a relatively dense set. We construct examples to show that subspace-hypercyclicity…

Let $a$ be a semi-almost periodic matrix function with the almost periodic representatives $a_l$ and $a_r$ at $-\infty$ and $+\infty$, respectively. Suppose $p:\mathbb{R}\to(1,\infty)$ is a slowly oscillating exponent such that the Cauchy…

We prove an abstract theorem of maximal hypoellipticy showing that in an abstract calculus under some natural assumptions, an operator is maximally hypoelliptic if and only if its principal symbol is left invertible. We then show that our…

Suppose that ${\cal L}$ is a divergence form differential operator of the form ${\cal L}f:=(1/2) e^{U}\nabla_x\cdot\big[e^{-U}(I+H)\nabla_x f\big]$, where $U$ is scalar valued, $I$ identity matrix and $H$ an anti-symmetric matrix valued…

The paper describes various approaches to the invertibility of Toeplitz plus Hankel operators in Hardy and $l^p$-spaces, integral and difference Wiener-Hopf plus Hankel operators and generalized Toeplitz plus Hankel operators. Special…

In this paper, we prove that if $T$ is diskcyclic operator then the closed unit disk multiplied by the union of the numerical range of all iterations of $T$ is dense in $\mathcal H$. Also, if $T$ is diskcyclic operator and $|\lambda|\le 1$,…

We prove that on $\mathbb{R}^n$, there is no $N$-supercyclic operator with $1\leq N< \lfloor \frac{n+1}{2}\rfloor$ i.e. if $\mathbb{R}^n$ has an $N$ dimensional subspace whose orbit under $T$ is dense in $\mathbb{R}^n$, then $N$ is greater…

This paper considers weak supercyclicity for bounded linear operators on a normed space. On the one hand, weak supercyclicity is investigated for classes of Hilbert-space operators: (i) self-adjoint operators are not weakly supercyclic,…

A linear different operator L is called weakly hypoelliptic if any local solution u of Lu=0 is smooth. We allow for systems, that is, the coefficients may be matrices, not necessarily of square size. This is a huge class of important…

The invertibility of Wiener-Hopf plus Hankel operators $W(a)+H(b)$ acting on the spaces $L^p(\mathbb{R}^+)$, $1 < p<\infty$ is studied. If $a$ and $b$ belong to a subalgebra of $L^\infty(\mathbb{R})$ and satisfy the condition…