Related papers: Dynamics of inner functions revisited
We study ergodic and mixing properties of non-autonomous dynamics on the unit circle generated by inner functions fixing the origin.
Analytic self-maps of the unit disc whose hyperbolic derivative is uniformly bounded by a constant smaller than one, are called contractive. We describe these maps in terms of their Aleksandrov-Clark measures and in terms of their…
It is a classical result that Lebesgue measure on the unit circle is invariant under inner functions fixing the origin. In this setting, the distortion of Hausdorff contents has also been studied. We present here similar results focusing on…
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 systems. Several classes of examples are provided.
We study the invariant subspaces generated by inner functions for a class of $\mathcal{P}^t(\mu)$-spaces which can be identified as spaces of analytic functions in the unit disk $\mathbb{D}$, where $\mu$ is a measure supported in the closed…
This study deals with continuous limits of interacting one-dimensional diffusive systems, arising from stochastic distortions of discrete curves with various kinds of coding representations. These systems are essentially of a…
Let $\mathscr J$ be the space of inner functions of finite entropy endowed with the topology of stable convergence. We prove that an inner function $F \in \mathscr J$ possesses a radial limit (and in fact, a minimal fine limit) in the unit…
The main aim of this paper is to establish the connection between well-known criteria for the pseudocontinuability of a non-inner Schur function Theta in the unit disk. In a canonical way we associate a probability measure mu on the unit…
We continue the study of analytic functions in the unit disk of finite order with arbitrary set of singular points on the unit circle, introduced in \cite{FG}. The main focus here is made upon the inverse problem: the existence of a…
This article consists of two connected parts. In the first part, we study the shift invariant subspaces in certain $\mathcal{P}^2(\mu)$-spaces, which are the closures of analytic polynomials in the Lebesgue spaces $\mathcal{L}^2(\mu)$…
We show the existence of singular inner functions that are cyclic in some Besov-type spaces of analytic functions over the unit disc. Our sufficient condition is stated only in terms of the modulus of smoothness of the underlying measure.…
The sensitivity properties of intermittent control are analysed and the conditions for a limit cycle derived theoretically and verified by simulation.
We study stochastic systems characterized by difference inclusions. Such stochastic differential inclusions are defined by set-valued maps involving the current state and stochastic input. For such systems, we investigate the problem of…
In the setup of i.i.d.~observations and a real valued differentiable functional~$T$, locally asymptotic upper bounds are derived for the power of one-sided tests (simple, versus large values of~$T$)and for the confidence probability of…
We introduce the concept of functions of locally bounded variation on abstract Wiener spaces and study their properties. Some nontrivial examples and applications to stochastic analysis are also discussed.
The Central Limit Theorem for Iterated Functions Systems on the circle is proved. We study also ergodicity of such systems.
We study the local Dirichlet integral of distance functions and their behavior within the harmonic Dirichlet space. We provide estimates for the local Dirichlet integral of distance functions, which allow us to study their membership in the…
We study functional limit theorems for linear type processes with short memory under the assumption that the innovations are dependent identically distributed random variables with infinite variance and in the domain of attraction of stable…
Functionals that strive to correct for such self-interaction errors, such as those obtained by imposing the Perdew-Zunger self-interaction correction or the generalized Koopmans' condition, become orbital dependent or orbital-density…
We present a systematic study on a class of nonlocal integral functionals for functions defined on a bounded domain and the naturally induced function spaces. The function spaces are equipped with a seminorm depending on finite differences…