43 citations · 47 across the 8 of their papers we have counts for
13 papers
Kitai's Criterion for Composition Operators
Daniel Gomes, Karl-G. Grosse-Erdmann
We present a general and natural framework to study the dynamics of composition operators on spaces of measurable functions, in which we then reconsider the characterizations for h…
A note on the Wiman-Valiron inequality
Karl-G. Grosse-Erdmann
The Wiman-Valiron inequality relates the maximum modulus of an analytic function to its Taylor coefficients via the maximum term. After a short overview of the known results, we ob…
Rate of growth of random analytic functions, with an application to linear dynamics
Kevin Agneessens, Karl-G. Grosse-Erdmann
We obtain Wiman-Valiron type inequalities for random entire functions and for random analytic functions on the unit disk that improve a classical result of Erdős and Rényi and rece…
Chaotic weighted shifts on directed trees
Karl-G. Grosse-Erdmann, Dimitris Papathanasiou
We study the dynamical behaviour of weighted backward shift operators defined on sequence spaces over a directed tree. We provide a characterization of chaos on very general Fréche…
Dynamics of weighted shifts on directed trees
Karl-G. Grosse-Erdmann, Dimitris Papathanasiou
We study the dynamical behaviour of weighted shifts defined on sequence spaces of a directed tree. In particular, we characterize their boundedness as well as when they are hypercy…
Zero-one law of orbital limit points for weighted shifts
Antonio Bonilla, Rodrigo Cardeccia, Karl-G. Grosse-Erdmann +1
Chan and Seceleanu have shown that if a weighted shift operator on , , admits an orbit with a non-zero limit point then it is hypercyclic. We pr…
Frequently recurrent operators
Antonio Bonilla, Karl-G. Grosse-Erdmann, Antoni López-Martínez +1
Motivated by a recent investigation of Costakis et al. on the notion of recurrence in linear dynamics, we study various stronger forms of recurrence for linear operators, in partic…
Chaos and frequent hypercyclicity for weighted shifts
Stéphane Charpentier, Karl Grosse-Erdmann, Quentin Menet
Bayart and Ruzsa [Ergodic Theory Dynam. Systems 35 (2015)] have recently shown that every frequently hypercyclic weighted shift on is chaotic. This contrasts with an earli…
Algebras of frequently hypercyclic vectors
Javier Falcó, Karl-G. Grosse-Erdmann
We show that the multiples of the backward shift operator on the spaces , , or , when endowed with coordinatewise multiplication, do not possess fr…
Algebrability of the set of hypercyclic vectors for backward shift operators
Javier Falcó, Karl-G. Grosse-Erdmann
We study the existence of algebras of hypercyclic vectors for weighted backward shifts on Fréchet sequence spaces that are algebras when endowed with coordinatewise multiplication…
Frequently hypercyclic bilateral shifts
Karl-G. Grosse-Erdmann
It is not known if the inverse of a frequently hypercyclic bilateral weighted shift on is again frequently hypercyclic. We show that the corresponding problem for…
Upper frequent hypercyclicity and related notions
Antonio Bonilla, Karl-G. Grosse-Erdmann
Enhancing a recent result of Bayart and Ruzsa we obtain a Birkhoff-type characterization of upper frequently hypercyclic operators and a corresponding Upper Frequent Hypercyclicity…
The pricing of lookback options and binomial approximation
Karl Grosse-Erdmann, Fabien Heuwelyckx
Refining a discrete model of Cheuk and Vorst we obtain a closed formula for the price of a European lookback option at any time between emission and maturity. We derive an asymptot…