Related papers: Generalized vector valued almost periodic and ergo…

Let $A$ be a general expansive matrix and $X$ be a ball quasi-Banach function space on $\mathbb R^n$, whose certain power (namely its convexification) supports a Fefferman--Stein vector-valued maximal inequality and the associate space of…

We consider random fields indexed by finite subsets of an amenable discrete group, taking values in the Banach-space of bounded right-continuous functions. The field is assumed to be equivariant, local, coordinate-wise monotone, and almost…

Let $\{T^z\}$ be an ergodic action of the group $Z^n$ by automorphisms of the probability space $(X,m)$, $\sum_{i}^\infty a_i<\infty$, $a_i>0$. For any sequence $M_k\to +\infty$ there exist $N_k>M_k$ and a function $ f\in L_1(X,m)$ such…

Given an m-dimensional compact submanifold $\mathbf{M}$ of Euclidean space $\mathbf{R}^s$, the concept of mean location of a distribution, related to mean or expected vector, is generalized to more general $\mathbf{R}^s$-valued functionals…

We consider the class GM(2b) in pointwise estimate of the deviations in strong mean of almost periodic functions from matrix means of partial sums of their Fourier series.

This paper is to characterize piecewise continuous almost periodic functions as the product of Bohr almost periodic functions and sequences. As an application, the result is used to discuss piecewise continuous almost periodic solutions of…

In this thesis, two $\bar{\mathbb{Q}}_\ell$-local systems, $\vphantom{\mathcal{E}}^\circ \mathcal{E}$ and $\vphantom{E}^\circ \mathcal{E}^\prime$ on the regular unipotent subvariety $\mathcal{U}_{0,K}$ of $p$-adic $\operatorname{SL}_2(K)$…

In our previous work, we studied the Generalized Hypergeometric Distribution (GHGD), which we refer to as the Multi-set Allocation Occupancy (MAO) distribution. We derived formulas for its expectation and variance for any number of subsets…

We study the finite dimensional spaces $V$ which are invariant under the action of the finite differences operator $\Delta_h^m$. Concretely, we prove that if $V$ is such an space, there exists a finite dimensional translation invariant…

In this paper, we survey physically related applications of a class of weighted quasi-Monte Carlo methods from a theoretical, deterministic perspective, and establish quantitative universal rapid convergence results via various regularity…

The main aim of this paper is to consider the classes of quasi-asymptotically almost periodic functions and Stepanov quasi-asymptotically almost periodic functions in Banach spaces. These classes extend the well known classes of…

In this paper, we analyze the classes of $({\mathrm R},{\mathcal B})$-multi-almost automorphic functions and asymptotically $({\mathrm R},{\mathcal B})$-multi-almost automorphic functions. We provide plenty valuable applications to the…

We prove a version of both Jacobi's and Montel's Theorems for the case of continuous functions defined over the field $\mathbb{Q}_p$ of $p$-adic numbers. In particular, we prove that, if \[ \Delta_{h_0}^{m+1}f(x)=0 \ \ \text{for all}…

Given a base manifold $M$ and a Lie group $G$, we define $\bar{\cal A}^H_M$ a space of generalized $G$-connections on $M$ with the following properties: - The space of smooth connections ${\cal A}^\infty_M = \sqcup_\pi {\cal A}^\infty_\pi$…

We give a general categorical construction that yields several monads of measures and distributions as special cases, alongside several monads of filters. The construction takes place within a categorical setting for generalized functional…

Let $f=(f^x\mid x\in S)$, $S\subset\mathbb{Z}^m$, be a semigroup of ergodic measure-preserving transformations of a probability space $(\Omega,\mathsf{P})$ and $h$ a real random function on $S$, such that $h(x+y,\omega)\le…

Let $S(z)$ be an absolutely convergent Dirichlet series with a bounded spectrum and only real zeros $a_n$, let $\mu$ be the sum of unit masses at points $a_n$. It is proven that the Fourier transform $\hat\mu$ in the sense of distributions…

In an effort to extend classical Fourier theory, Hedenmalm and Montes-Rodr\'{\i}guez (2011) found that the function system \[ e_m(x)=e^{i\pi mx},\quad e_n^\dagger(x)=e_n(-1/x)=e^{-i\pi n/x} \] is weak-star complete in…

We extend the Matom\"{a}ki-Radziwi\l\l{} theorem to a large collection of unbounded multiplicative functions that are uniformly bounded, but not necessarily bounded by 1, on the primes. Our result allows us to estimate averages of such a…

We construct an exemple of a full factor $M$ such that its canonical outer modular flow $\sigma^M : \mathbb{R} \rightarrow \mathrm{Out}(M)$ is almost periodic but $M$ has no almost periodic state. This can only happen if the discrete…