Related papers: On Bochner's Almost-periodicity criterion

We introduce and study a dimensional-like characteristic of an uniformly almost periodic function, which we call the Diophantine dimension. By definition, it is the exponent in the asymptotic behavior of the inclusio length. Diophantine…

This is the second part of a work dedicated to the study of Bernstein-Sato polynomials for several analytic functions depending on parameters. In this part, we give constructive results generalizing previous ones obtained by the author in…

We study meromorphic functions in a strip almost periodic with respect to the spherical metric. Then we get a complete description of zeros and poles for this class of functions, find a condition for a meromorphic almost periodic function…

This paper deals with fundamental properties of Poincar\'e half-maps defined on a straight line for planar linear systems. Concretely, we focus on the analyticity of the Poincar\'e half-maps, their series expansions (Taylor and…

We show that an $R^d$-topological dynamical system equipped with an invariant ergodic measure has discrete spectrum if and only it is $\mu$-mean equicontinuous (proven for $Z^d$ before). In order to do this we introduce mean equicontinuity…

By using the method of Loewner chains, we establish some sufficient conditions for the analyticity and univalency of functions defined by an integral operator. Also, we refine the result to a quasiconformal extension criterion with the help…

This paper is devoted to the study of the stochastic properties of dynamical systems preserving an infinite measure. More precisely we prove central limit theorems for Birkhoff sums of observables of $\mathbb{Z}^2$-extensions of dynamical…

This article describes a method for constructing approximations to periodic solutions of dynamic Lorenz system with classical values of the system parameters. The author obtained a system of nonlinear algebraic equations in general form…

We present two possible criteria quantifying the degree of classicality of an arbitrary (finite dimensional) dynamical system. The inputs for these criteria are the classical dynamical structure of the system together with the quantum and…

The stochastic expansion of the marginal quasi-likelihood function associated with a class of generalized linear models is shown. Based on the expansion, a quasi-Bayesian information criterion is proposed that is able to deal with…

We supplement the result of the first part of the work with estimates of the integrals of the difference of subharmonic functions in measure with some deterioration of the absolute constants, but these estimates have the form of a…

First, we give the definition for quasi-nearly subharmonic functions, now for general, not necessarily nonnegative functions, unlike previously. We point out that our function class incudes, among others, quasisubharmonic functions, nearly…

We establish a link between the basic properties of the discriminant of periodic second-order differential equations and an elementary analysis of Herglotz functions. Some generalizations are presented using the language of self-adjoint…

We extend some definitions and give new results about the theory of slice analysis in several quaternionic variables. The sets of slice functions which are respectively slice, slice regular and circular w.r.t. given variables are…

In this paper we determine the Bochner measure for spherical functions on a semi-simple Lie group of rank one.

This paper uses the machinery of almost periodic functions to prove that even without uniform convergence the connection between a pair of almost periodic functions and the constants of the associated Fourier series exists for both the…

We obtain a criterion for the quasi-regularity of generalized (non-sectorial) Dirichlet forms, which extends the result of P.J. Fitzsimmons on the quasi-regularity of (sectorial) semi-Dirichlet forms. Given the right (Markov) process…

We present a new elementary proof of a theorem due to Harald Bohr, which states that an unbounded, analytic, and almost periodic function in a half-plane can be written as the sum of two analytic functions: the first is unbounded and…

For a class of $\mathbb{R}^d$-ations and $\mathbb{Z}^d$-actions on the $n$-dimensional torus $\mathbb{T}^n$, we characterize their unique ergodicity and establish a theorem of Weyl type. This result allows us to establish an isomorphism…

The classical criterion for compactness in Banach spaces of functions can be reformulated into a simple tightness condition in the time-frequency domain. This description preserves more explicitly the symmetry between time and frequency…