Results 21 to 30 of about 2,965 (120)
, 2014 We generalize a result for the translation $C_0$-semigroup on $L^p(\R_+,\mu)$ about the equivalence of being chaotic and satisfying the Frequent Hypercyclicity criterion due to Mangino and Peris to certain weighted composition $C_0$-semigroups. Such $C_0$
Kalmes, Thomas
core +1 more source
Existence of common and upper frequently hypercyclic subspaces [PDF]
, 2014 We provide criteria for the existence of upper frequently hypercyclic subspaces and for common hypercyclic subspaces, which include the following consequences.
Bès, Juan, Menet, Quentin
core +1 more source
Hypercyclic Behavior of Translation Operators on Spaces of Analytic Functions on Hilbert Spaces
Journal of Function Spaces, Volume 2015, Issue 1, 2015., 2015 We consider special Hilbert spaces of analytic functions of many infinite variables and examine composition operators on these spaces. In particular, we prove that under some conditions a translation operator is bounded and hypercyclic.
Zoryana Mozhyrovska +2 more
wiley +1 more source
Difference sets and frequently hypercyclic weighted shifts [PDF]
, 2013 We solve several problems on frequently hypercyclic operators. Firstly, we characterize frequently hypercyclic weighted shifts on $\ell^p(\mathbb Z)$, $p\geq 1$.
Bayart, Frédéric, Ruzsa, Imre
core +3 more sources
Chaos for Cosine Operator Functions on Groups
Abstract and Applied Analysis, Volume 2014, Issue 1, 2014., 2014 Let 1 ≤ p < ∞ and G be a locally compact group. We characterize chaotic cosine operator functions, generated by weighted translations on the Lebesgue space Lp(G), in terms of the weight condition. In particular, chaotic cosine operator functions and chaotic weighted translations can only occur simultaneously.
Chung-Chuan Chen, Wei-Shih Du
wiley +1 more source
Monsters in Hardy and Bergman spaces [PDF]
, 2002 A monster in the sense of Luh is a holomorphic function on a simply connected domain in the complex plane such that it and all its derivatives and antiderivatives exhibit an extremely wild behaviour near the boundary.
Bernal González, Luis +1 more
core +1 more source
An Extension of Hypercyclicity for N‐Linear Operators
Abstract and Applied Analysis, Volume 2014, Issue 1, 2014., 2014 Grosse‐Erdmann and Kim recently introduced the notion of bihypercyclicity for studying the existence of dense orbits under bilinear operators. We propose an alternative notion of orbit for N‐linear operators that is inspired by difference equations. Under this new notion, every separable infinite dimensional Fréchet space supports supercyclic N‐linear ...
Juan Bès +2 more
wiley +1 more source
Hypercyclicity Criterion on Basic Elementary Operator
Journal of Advances in Mathematics and Computer ScienceHypercyclicity criterion has been an important tool in the test of hypercyclicity of different operators. This tool has been used by different mathematicians to show that generalized derivations, left and right multiplication operators, operator algebra ...
Kawira Esther +2 more
semanticscholar +1 more source
Powers of Convex‐Cyclic Operators
Abstract and Applied Analysis, Volume 2014, Issue 1, 2014., 2014 A bounded operator T on a Banach space X is convex cyclic if there exists a vector x such that the convex hull generated by the orbit Tnxn≥0 is dense in X. In this note we study some questions concerned with convex‐cyclic operators. We provide an example of a convex‐cyclic operator T such that the power Tn fails to be convex cyclic.
Fernando León-Saavedra +2 more
wiley +1 more source
Dynamics of tuples of matrices [PDF]
, 2008 In this article we answer a question raised by N. Feldman in \cite{Feldman} concerning the dynamics of tuples of operators on $\mathbb{R}^n$. In particular, we prove that for every positive integer $n\geq 2$ there exist $n$ tuples $(A_1, A_2, ..., A_n ...
Costakis, George +2 more
core +1 more source