Related papers: Strongly $n$-supercyclic operators
Multiple scalar integral representations for traces of operator derivatives are obtained and applied in the proof of existence of the higher order spectral shift functions.
In [9] a question is raised: if a power bounded operator is quasisimilar to a singular unitary operator, is it similar to this unitary operator? For polynomially bounded operators, a positive answer to this question is known [1], [13]. In…
Several quantum systems have been used in the last few years to extend supersymmetry. In this paper we show all this systems fit into the picture of what we call "Number Operator Algebras".
Spectral properties of many finite convolution integral operators have been understood by finding differential operators that commute with them. In this paper we compile a complete list of such commuting pairs, extending previous work to…
The purpose of the present work is to answer an open problem which is raised by G.Costakis and A.Manoussos in their paper "J-class operators and hypercyclicity " accepted by J. Operator Theory. More precisely, we give the spectral…
A new type of combinations of Bernstein operators is given in [1]. Here, we introduce another one, which can be used to approximate the functions with singularities. The direct and inverse results of the weighted approximation of this new…
In this paper we revisit the construction of supersymmetric Schwarzians using nonlinear realizations. We show that ${\cal N}=0,1,2,3,4$ supersymmetric Schwarzians can be systematically obtained as certain projections of Maurer-Cartan forms…
We prove that a bounded operator $T$ on a separable Banach space $X$ satisfying a strong form of the Frequent Hypercyclicity Criterion (which implies in particular that the operator is universal in the sense of Glasner and Weiss) admits…
In this paper, we study some properties of a certain kind of permutation $\sigma$ over $\mathbb{F}_{2}^{n}$, where $n$ is a positive integer. The desired properties for $\sigma$ are: (1) the algebraic degree of each component function is…
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…
In this paper we consider a problem of the similarity of complex symmetric operators to perturbations of restrictions of normal operators. For a subclass of cyclic complex symmetric operators in a finite-dimensional Hilbert space we prove…
We study the numerical range of bounded linear operators on quaternionic Hilbert spaces and its relation with the S-spectrum. The class of complex operators on quaternionic Hilbert spaces is introduced and the upper bild of normal complex…
We study the existence of hypercyclic algebras for convolution operators $\Phi(D)$ on the space of entire functions whose symbol $\Phi$ has unimodular constant term. In particular, we provide new eigenvalue criteria for the existence of…
We review the spin bit model describing anomalous dimensions of the operators of Super Yang--Mills theory. We concentrate here on the scalar sector. In the limit of large $N$ this model coincides with integrable spin chain while at finite N…
We establish a spectral characterization theorem for the operators on complex Hilbert spaces of arbitrary dimensions that attain their norm on every closed subspace. The class of these operators is not closed under addition. Nevertheless,…
We define strongly continuous max-additive and max-plus linear operator semigroups and study their main properties. We present some important examples of such semigroups coming from non-linear evolution equations.
We discuss the class of superconductors which have pairing correlations which are odd in frequency, as introduced originally by Berezinskii and more recently by Balatsky and Abrahams. As follows from the equations of motion, a natural…
The modular forms and weighted densities over the 1-dimensional manifold $M$ are transformed ``alike" under the group of linear fractional changes of coordinates, so the classifications of differential operators between spaces of (A)…
We discuss several open problems on spectrally bounded operators, some new, some old, adding in a few new insights.
This paper reports a theory of Koopman operators for a class of hybrid dynamical systems with globally asymptotically stable periodic orbits, called hybrid limit-cycling systems. We leverage smooth structures intrinsic to the hybrid…