Results 141 to 150 of about 1,147,699 (174)

Property (ω) and Hypercyclic Property for Operators

Wuhan University Journal of Natural Sciences
By means of the new spectrum defined with respect to the property of Consistence in Fredholm and Index (CFI) around an operator, we establish the necessary and sufficient conditions for a bounded linear opeator [see formula in PDF] defined on a Hilbert ...
Lei Dai, Jialu Yi
semanticscholar   +1 more source

Frequently hypercyclic operators

2011
The contents of this chapter are motivated by recent work on the application of ergodic theory to linear dynamics. While the technical difficulties involved prevent us from studying these tools here, we will discuss a new concept that has come out of these investigations, the frequently hypercyclic operators.
Karl-G. Grosse-Erdmann, Alfred Peris Manguillot   +1 more
openaire   +1 more source

Weyl type theorems for hypercyclic, supercyclic, and Toeplitz operators

Advances in Operator Theory
In this paper, we study property (UWE)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt ...
Simi Thomas, Thankarajan Prasad, Shery Fernandez   +2 more
semanticscholar   +1 more source

Hypercyclic and Chaotic Convolution Operators

Journal of the London Mathematical Society, 2000
Every convolution operator on a space of ultradifferentiable functions of Beurling or Roumieu type and on the corresponding space of ultradistributions is hypercyclic and chaotic (i.e., it is transitive and has a dense set of periodic points) when it is not a multiple of the identity.
openaire   +2 more sources

Faber-hypercyclic semigroups of linear operators

Filomat
In this research, the ?-hypercyclic and ?-transitive behavior are studied within the framework of linear strongly continuous semigroups. We give sufficient constraints on the spectrum of an operator to yield a ?-hypercyclic semigroup.
N. Karim, O. Benchiheb, M. Amouch
semanticscholar   +1 more source

On Hypercyclic Operators in Weighted Spaces of Infinitely Differentiable Functions

Mathematical Notes, 2023
Алсу Ильдаровна Рахимова, A. I. Rakhimova   +1 more
semanticscholar   +1 more source

Existence of hypercyclic operators

2011
In this chapter we obtain, among other things, the Ansari–Bernal theorem that every infinite-dimensional separable Banach space supports a hypercyclic operator. In contrast, some infinite-dimensional separable Banach spaces do not support any chaotic operator. We also discuss here the richness of the set of hypercyclic operators in two ways: it forms a
Karl-G. Grosse-Erdmann, Alfred Peris Manguillot   +1 more
openaire   +1 more source

Powers of Hypercyclic Functions for Some Classical Hypercyclic Operators

Integral Equations and Operator Theory, 2007
We show that no power of any entire function is hypercyclic for Birkhoff’s translation operator on $$\mathcal{H}(\mathbb{C})$$ . On the other hand, we see that the set of functions whose powers are all hypercyclic for MacLane’s differentiation operator is a Gδ ...
R. M. Aron, J. A. Conejero, A. Peris, J. B. Seoane–Sepúlveda   +3 more
openaire   +1 more source

Some Examples of Hypercyclic Operators and Universal Sequences of Operators

Topological Dynamics and Topological Data Analysis, 2021
Kit C. Chan
semanticscholar   +1 more source

Hypercyclic and chaotic operators

2011
In this chapter, the notions and results from the first chapter are revisited in the context of linearity. We introduce the notion of a hypercyclic operator and that of a chaotic operator. Among other things it is proved that the classical operators of Birkhoff, MacLane and Rolewicz are chaotic; it is shown that every hypercyclic operator possesses a ...
Karl-G. Grosse-Erdmann, Alfred Peris Manguillot   +1 more
openaire   +1 more source