Related papers: Beurling density theorems for sampling and interpo…

We introduce a large family of reproducing kernel Hilbert spaces $\mathcal{H} \subset \mbox{Hol}(\mathbb{D})$, which include the classical Dirichlet-type spaces $\mathcal{D}_\alpha$, by requiring normalized monomials to form a Riesz basis…

We investigate the reproducing properties of Gabor systems within the context of expansible groups. These properties are established in terms of density conditions. The concept of density that we employ mirrors the well-known Beurling…

This paper begins the study of infinite-dimensional modules defined on bicomplex numbers. It generalizes a number of results obtained with finite-dimensional bicomplex modules. The central concept introduced is the one of a bicomplex…

Let $\mathcal{M}$ be a semifinite von Nemann algebra equipped with an increasing filtration $(\mathcal{M}_n)_{n\geq 1}$ of (semifinite) von Neumann subalgebras of $\mathcal{M}$. For $0<p <\infty$, let $\mathsf{h}_p^c(\mathcal{M})$ denote…

A harmonically trapped Bose-Einstein condensate (BEC) leads to topologically trivial compact states. Because of the long-range nonlocal dipole-dipole interaction, a strongly dipolar BEC revealed many novel phenomena. Here we show that in a…

In this work, we introduce the $\beta$-semigroup for $\beta > 0$, which unifies and extends the classical Poisson (for $\beta=1$) and heat (for $\beta=2$) semigroups within the Dunkl analysis framework. Leveraging this semigroup, we derive…

Following a recent idea by Ball, we introduce the notion of strongly truncated Riesz space with a suitable spectrum. We prove that, under an extra Archimedean type condition, any strongly truncated Riesz space is isomorphic to a uniformly…

We formulate and implement Cyclic Density Functional Theory (Cyclic DFT) -- a self-consistent first principles simulation method for nanostructures with cyclic symmetries. Using arguments based on Group Representation Theory, we rigorously…

Let $D$ be a bounded domain in ${\Bbb R}^n$ whose boundary has a Minkowski dimension $\alpha<n$. Suppose that $E_{\Lambda}= {\{e^{2 \pi i x \cdot \lambda}\}}_{\lambda \in \Lambda}$, $\Lambda$ an infinite discrete subset of ${\Bbb R}^n$, is…

The intrinsic volumes induced by a stationary Poisson k-flat process inside a compact and convex sampling window are considered. Using techniques from stochastic analysis, more precisely calculus with multiple stochastic integrals and a…

In this paper we introduce complex minimal Lagrangian surfaces in the bi-complex hyperbolic space and study their relation with representations in $\mathrm{SL}(3,\mathbb{C})$. Our theory generalizes at the same time minimal Lagrangian…

Let $U_q(\frak{g})$ a the quantum affine algebra of type $A_n^{(1)}$, $A_{2n-1}^{(2)}$, $A_{2n}^{(2)}$, $B_n^{(1)}$, $D_n^{(1)}$ and $D_{n+1}^{(2)}$, and let $\mathcal{F}(\Lambda)$ be the Fock space representation for a level 1 dominant…

We study the von Neumann algebra description of the inflationary quasi-de Sitter (dS) space. Unlike perfect dS space, quasi-dS space allows the nonzero energy flux across the horizon, which can be identified with the expectation value of…

Let $Z$ be a Boolean model based on a stationary Poisson process $\eta$ of compact, convex particles in Euclidean space ${\mathbb{R}}^d$. Let $W$ denote a compact, convex observation window. For a large class of functionals $\psi$, formulas…

We give an application of a topological dynamics version of multidimensional Brown's lemma to tiling theory: given a tiling of an Euclidean space and a finite geometric pattern of points $F$, one can find a patch such that, for each scale…

Some basic features of the simultaneous inclusion of discrete fibrations and discrete opfibrations on a category A in the category of categories over A are studied; in particular, the reflections and the coreflections of the latter in the…

We characterize the model spaces $K_\Theta$ in which functions with smooth boundary extensions are dense. It is shown that such approximations are possible if and only if the singular measure associated to the singular inner factor of…

Although numerous studies have focused on normal Besov spaces, limited studies have been conducted on exponentially weighted Besov spaces. Therefore, we define exponentially weighted Besov space $VB_{p,q}^{\delta,w}(\mathbb{R}^d)$ whose…

We give a short proof of the $L^{1}$ criterion for Beurling generalized integers to have a positive asymptotic density. We actually prove the existence of density under a weaker hypothesis. We also discuss related sufficient conditions for…

We obtain a fundamental measure density functional for mixtures of parallel hard cylinders. To this purpose we first generalize to multicomponent mixtures the fundamental measure functional proposed by Tarazona and Rosenfeld for a…