Related papers: Hypercyclic behavior of some non-convolution opera…
The purpose of the present work is to treat a new notion related to linear dynamics, which can be viewed as a "localization" of the notion of hypercyclicity. In particular, let $T$ be a bounded linear operator acting on a Banach space $X$…
For lattice operators that are relevant to the calculation of moments of nucleon structure functions we investigate the transformation properties under the hypercubic group. We give explicit bases of irreducible subspaces for tensors of…
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,…
We study the description of semicommutative Hardy spaces in terms of molecules. We use this characterization to obtain $\mathrm{H}_1^c - \mathrm{H}_1^c$ estimates for Calder\'on-Zygmund operators with kernels with values in a semifinite von…
In this paper, we study a natural class of groups that act as affine transformations of $\mathbb T^N$. We investigate whether these solvable, "abelian-by-cyclic," groups can act smoothly and nonaffinely on $\mathbb T^N$ while remaining…
We find and classify possible equivariant spin structures with Dirac operators on the noncommutative torus, proving that similarly as in the classical case the spectrum of the Dirac operator depends on the spin structure.
The analysis of branching problems for restriction of representations brings the concept of symmetry breaking transform and holographic transform. Symmetry breaking operators decrease the number of variables in geometric models, whereas…
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…
In this paper we study some dynamical properties such as Frequent Hypercyclicity Criterion, chaos, disjoint hypercyclicity and F-transitivity via Furstenberg family F for generalized bilateral weighted shift operator on the standard Hilbert…
. We study the statistical properties of the eigenvalues of non-Hermitian operators assoicated with the dissipative complex systems. By considering the Gaussian ensembles of such operators, a hierarchical relation between the correlators is…
Within a strong coupling expansion, we construct local quasi-conserved operators for a class of Hamiltonians that includes both integrable and non-integrable models. We explicitly show that at the lowest orders of perturbation theory the…
Let $\mathbf{A}$ be a bounded self-adjoint operator on a separable Hilbert space $\mathfrak{H}$ and $\mathfrak{H}_0\subset\mathfrak{H}$ a closed invariant subspace of $\mathbf{A}$. Assuming that $\mathfrak{H}_0$ is of codimension 1, we…
Some binary quadratic operads are endowed with anticyclic structures and their characteristic functions as anticyclic operads are determined, or conjectured in one case.
Let $B(H)$ be the algebra of bounded linear operators on a separable infinite-dimensional Hilbert space $H$. We study the commutant of $B(H)$ in its ultrapower. We characterize the class of non-principal ultrafilters for which this…
We propose a systematic scheme for computing the variation of rearrangement operators arising in the recently developed spectral geometry on noncommutative tori and $\theta$-deformed Riemannian manifolds. It can be summarized as a category…
We treat the question of existence of common hypercyclic vectors for families of continuous linear operators. It is shown that for any continuous linear operator $T$ on a complex Fr\'echet space $X$ and a set $\Lambda\subseteq \R_+\times\C$…
We study higher-order elliptic operators on one-dimensional ramified structures (networks). We introduce a general variational framework for fourth-order operators that allows us to study features of both hyperbolic and parabolic equations…
This paper explores various classes of invariant subspaces of the classical Ces\`{a}ro operator $C$ on the Hardy space $H^2$. We provide a new characterization of the finite co-dimensional $C$-invariant subspaces, based on earlier work of…
We introduce the notion of a family of convolution operators associated with a given elliptic partial differential operator. Such a convolution structure is shown to exist for a general class of Laplace-Beltrami operators on two-dimensional…
We introduce new aspects in conformal geometry of some very natural second-order differential operators. These operators are termed shift operators. In the flat space, they are intertwining operators which are closely related to symmetry…