Related papers: Ces\`aro-Hypercyclic and Weyl type theorem
We give an explicit formula for symplectically basic representatives of the cyclic cohomology of the Weyl algebra. This paper can be seen as cyclic addendum to the paper by Feigin, Felder and Shoikhet, where the analogous Hochschild case…
We describe holomorphic functions and fractional powers of Ces\'{a}ro operators in $L^2(\mathbb{R})$, $L^2(\mathbb{R}_+)$, and $L^2[0,1]$. Logarithms of Ces\'{a}ro operators are introduced as well and their spectral properties are studied.…
In this paper, we give a new approach for the study of Weyl-type theorems. Precisely we introduce the concepts of spectral valued and spectral partitioning functions. Using two natural order relations on the set of spectral valued…
In this paper, we obtain several extensions of semi-Fredholm theory on Hilbert modules by generalizing in this setting their classical counterparts regarding Weyl operators and Drazin invertible operators.
We develop the bivector formalism in higher dimensional Lorentzian spacetimes. We define the Weyl bivector operator in a manner consistent with its boost-weight decomposition. We then algebraically classify the Weyl tensor, which gives rise…
In this paper, which is a follow-up of our first paper "Normal forms for ordinary differential operators, I", we extend the theory of normal forms for non-commuting operators, and obtain as an application a commutativity criterion for…
We give necessary and sufficient condition so that we have d-hypercyclicity for operators who map a holomorphic function to a partial sum of the Taylor expansion. This problem is connected with doubly universal Taylors series and this is an…
This paper is concerned with the Weyl composition of symbols in large dimension. We specify a class of symbols in order to estimate the Weyl symbol of the product of two Weyl $h-$pseudodifferential operators, with constants independent of…
It is well known that the generalized Ces\`aro matrices of order one are hyponormal operators on $\ell^2$, and it has recently been shown that the Ces\`aro matrix of order two is also hyponormal. Here the relatively new concept of…
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,…
In this article we study the Ces\`{a}ro operator $$ \mathcal{C}(f)(z)=\frac{1}{z}\int_{0}^{z}f(\zeta)\,d\zeta, $$ and its companion operator $\mathcal{T}$ on Hardy spaces of the upper half plane. We identify $\mathcal{C}$ and $\mathcal{T}$…
We prove a mean value theorem for the traces of Hecke operators acting on cusp forms of GL(n) over imaginary quadratic number fields together with an upper bound for the error term depending explicitly on the Hecke operator.
A Lie superalgebrea of Riemannian type leads to a representation of a quadratic Lie algebra into a Weyl algebra. A necessary and sufficient condition that such a representation leads to a Lie superalgebra of Riemannian type is that the…
In this paper we prove amalgam Balian-Low theorems and Balian-Low type theorems on $L^2(\mathbb{C})$ for the special Hermite operator using the Weyl transform.
We investigate the harmonic analysis associated with the hyper-Bessel operator on C, and we prove the chaotic character of the related convolution operators.
The main aim of this paper is to prove a generalization of the classical Bohr theorem and as an application, we obtain a counterpart of Bohr theorem for the generalized Ces\'aro operator.
In the present paper we investigate different variants of supercyclicity, precisely $\mathbb R^+$-, $\mathbb R$- and $\mathbb C$-supercyclicity in the context of composition operators. We characterize $\mathbb R$-supercyclic composition…
We solve several problems on frequently hypercyclic operators. Firstly, we characterize frequently hypercyclic weighted shifts on $\ell^p(\mathbb Z)$, $p\geq 1$. Our method uses properties of the difference set of a set with positive upper…
In this paper, we give some necessary and sufficient conditions for weighted conditional expectation type operators on L2 to be centered. Also, we investigate the relation between normal and centered weighted con- ditional type operators.…
The aim of this article is to prove a Beals type characterization theorem for pseudodifferential operators in Wiener spaces. The definition of pseudodifferential operators in Wiener spaces and a Calder\'on-Vaillancourt type result appear in…