Related papers: On Bochner's Almost-periodicity criterion
The extension of Hille-Phillips functional calculus of semigroup generators which leads to unbounded operators is considered. Connections of this calculus to Bochner-Phillips functional calculus are indicated. In particular, the…
Whenever all differences between zeros of two holomorphic almost periodic functions in a strip form a discrete set, then both functions are infinite products of periodic functions with commensurable periods. In particular, the result is…
A criterion for comonadicity of the extension-of- scalars functor associated to an extension of (not necessarily commutative) rings is given. As an application of this criterion, some known results on the comonadicity of such functors are…
In this paper, we introduce concepts of pathwise random almost periodic and almost automorphic solutions for dynamical systems generated by non-autonomous stochastic equations. These solutions are pathwise stochastic analogues of…
We develop a comprehensive theory of reflectionless canonical systems with an arbitrary Dirichlet-regular Widom spectrum with the Direct Cauchy Theorem property. This generalizes, to an infinite gap setting, the constructions of finite gap…
This paper provides two results that are useful in the study of the existence and the stability properties of a periodic solution for a given dynamical system. The first result deals with scalar time-periodic systems and establishes the…
A generalization of Hurwitz stable polynomials to real rational functions is considered. We establishe an analogue of the Hurwitz stability criterion for rational functions and introduce a new type of determinants that can be treated as a…
Approximations of fractional Brownian motion using Poisson processes whose parameter sets have the same dimensions as the approximated processes have been studied in the literature. In this paper, a special approximation to the…
The paper is a survey of notions and results related to classical and new generalizations of the notion of a periodic sequence. The topics related to almost periodicity in combinatorics on words, symbolic dynamics, expressibility in logical…
We introduce a new generalization of Euler's $\varphi$-function associated with a system of polynomials of several variables. We reprove by a short direct approach certain known related identities, and study some other special cases that do…
This paper is a short survey of the recent results on examples of periodic two-dimensional continued fractions (in Klein's model). In the last part of this paper we formulate some questions, problems and conjectures on geometrical…
In this paper we consider several families of potential non-isochronous systems and study their associated period functions. Firstly, we prove some properties of these functions, like their local behavior near the critical point or…
We derive a necessary and sufficient condition for stochastic processes to have almost periodic finite dimensional distributions; in particular, we obtain characterizations for infinitely divisible processes to be almost periodic in terms…
In this paper, we analyze various classes of multi-dimensional $\rho$-almost periodic type functions $F : I \times X \rightarrow Y$ and multi-dimensional $(\omega,\rho)$-almost periodic type functions $F : I \times X \rightarrow Y,$ where…
In [19] there is an approach to the investigation of the pseudocontinuability of Schur functions in terms of Schur parameters. In particular, there was obtained a criterion for the pseudocontinuability of Schur functions and the Schur…
By introducing a max-plus dynamical system having limit cycles, we discuss their periodicity, especially the number of discrete states in them. We also find that quasi-periodic cycles exist depending on the bifurcation parameter in the…
We give a construction of Gabor type frames for suitable separable subspaces of the non-separable Hilbert spaces $AP_2({\mathbb R})$ of almost periodic functions of one variable. Furthermore we determine a non-countable generalized frame…
We consider certain finite sets of circle-valued functions defined on intervals of real numbers and estimate how large the intervals must be for the values of these functions to be uniformly distributed in an approximate way. This is used…
We consider metrizable ergodic topological dynamical systems over locally compact, $\sigma$-compact abelian groups. We study pure point spectrum via suitable notions of almost periodicity for the points of the dynamical system. More…
In this paper, we will discuss the notion of almost orthogonality in a functional sequence.Especially, we will define a few sequences of almost orthogonal polynomials which can be used successfully for modeling of electronic systems which…