5 papers
Discrete analogues in harmonic analysis: methods
Bartosz Langowski, Mariusz Mirek, Tomasz Z. Szarek
In this note we present how the almost-orthogonality methods based on arguments can be employed to study boundedness of discrete operators of Radon type. Almost-orthogonalit…
On a problem of Ö. Stenflo
Klaudiusz Czudek, Tomasz Szarek
We construct an e-chain on a locally compact space with the unique stationary distribution such that the strong law of large numbers does not hold. This answers negatively the ques…
Unique ergodicity for noninvertible function systems on an interval
Sander C. Hille, Hanna Oppelmayer, Tomasz Szarek
We study random dynamical systems of certain continuous functions on the unit interval. We use bounded variation to provide sufficient conditions for unique ergodicity of these sys…
Proximality, stability, and central limit theorem for random maps on an interval
Sander C. Hille, Katarzyna Horbacz, Hanna Oppelmayer +1
Stochastic dynamical systems consisting of non-invertible continuous maps on an interval are studied. It is proved that if they satisfy the recently introduced so-called -inject…
Unique ergodicity for random noninvertible maps on an interval
Sara Brofferio, Hanna Oppelmayer, Tomasz Szarek
In this short note, we investigate non-invertible stochastic dynamical systems on the unit interval . We provide a handy condition for unique ergodicity for systems that ar…