Related papers: Multi-tiling sets, Riesz bases, and sampling near …

We consider \textit{additive spaces}, consisting of two intervals of unit length or two general probability measures on ${\mathbb R}^1$, positioned on the axes in ${\mathbb R}^2$, with a natural additive measure $\rho$. We study the…

If G is a locally essential subgroup of a compact abelian group K, then: (i) t(G)=w(G)=w(K), where t(G) is the tightness of G; (ii) if G is radial, then K must be metrizable; (iii) G contains a super-sequence S converging to 0 such that…

We provide necessary and sufficient conditions for the space of smooth functions with compact supports $C^\infty_C(\Omega)$ to be dense in Musielak-Orlicz spaces $L^\Phi(\Omega)$ where $\Omega$ is an open subset of $\mathbb{R}^d$. In…

In this paper a sampling theory for unitary invariant subspaces associated to locally compact abelian (LCA) groups is deduced. Working in the LCA group context allows to obtain, in a unified way, sampling results valid for a wide range of…

Necessary and sufficient conditions are presented for several families of planar curves to form a set of stable sampling for the Bernstein space $\mathcal{B}_{\Omega}$ over a convex set $\Omega \subset \mathbb{R}^2$. These conditions…

Let $G$ be a connected linear algebraic group over a number field $K$. In this article, we study the almost strong approximation property (ASA) of $G$ raised by Rapinchuk and Tralle. Building on Demarche's results on strong approximation…

In this paper we prove an abstract homomorphism theorem for bilinear multipliers in the setting of locally compact Abelian (LCA) groups. We also provide some applications. In particular, we obtain a bilinear abstract version of K. de…

We present sufficient conditions on a smooth uniformly flat hypersurface W in the unit ball to be an interpolation hypersurface or a sampling hypersurface for generalized Bergman spaces associated to the unit ball with its Bergman metric.…

Fuglede's conjecture states that for a subset $\Omega$ of a locally compact abelian group $G$ with positive and finite Haar measure, there exists a subset of the dual group of $G$ which is an orthogonal basis of $L^{2}(\Omega)$ if and only…

We show that the sequential closure of a family of probability measures on the canonical space of c{\`a}dl{\`a}g paths satisfying Stricker's uniform tightness condition is a weak${}^*$ compact set of semimartingale measures in the pairing…

The family of harmonic Hilbert spaces is a natural enlargement of those classical $L^{2}$-Sobolev space on $\R^d$ which consist of continuous functions. In the present paper we demonstrate that the use of basic results from the theory of…

In this work, we provide some novel results that establish both the existence of Henig global proper efficient points and their density in the efficient set for vector optimization problems in arbitrary normed spaces. Our results do not…

In a recent breakthrough, Kelley and Meka (FOCS 2023) obtained a strong upper bound on the density of sets of integers without nontrivial three-term arithmetic progressions. In this work, we extend their result, establishing similar bounds…

By using ergodic theoretic techniques following Hillel F\"{u}rstenberg, we prove that measurable subsets of a locally compact abelian group of positive upper density contain Szemer\'{e}di-wise configurations defined by an arbitrary compact…

Let $(I,+)$ be a finite abelian group and $\mathbf{A}$ be a circular convolution operator on $\ell^2(I)$. The problem under consideration is how to construct minimal $\Omega \subset I$ and $l_i$ such that $Y=\{\mathbf{e}_i,…

We consider the Fock space weighted by $e^{-\alpha |z|^{2}}$, of entire and quasi-periodic (modulo a weight dependent on $\nu $) functions on ${C}$. The quotient space $\mathbb{C}/\mathbb{Z}$, called `The flat cylinder', is represented by…

For an abelian topological group G let G^* denote the dual group of all continuous characters endowed with the compact open topology. Given a closed subset X of an infinite compact abelian group G such that w(X) < w(G) and an open…

According to Comfort, Raczkowski and Trigos-Arrieta, a dense subgroup D of a compact abelian group G determines G if the restriction homomorphism G^ --> D^ of the dual groups is a topological isomorphism. We introduce four conditions on D…

Let $G$ be a simple algebraic group over an algebraically closed field $k$ and let $C_1, \ldots, C_t$ be non-central conjugacy classes in $G$. In this paper, we consider the problem of determining whether there exist $g_i \in C_i$ such that…

We present forms of the classical Riesz-Kolmogorov theorem for compactness that are applicable in a wide variety of settings. In particular, our theorems apply to classify the precompact subsets of the Lebesgue space $L^2$, Paley-Wiener…