5 papers
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…
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…