arXiv subjects

J. Antezana

Publications and source records attributed to J. Antezana.

4 recordsLinked to original sources

arXiv2026

Functions of Bounded Variation and Point Processes

We investigate the relationship between the analytical properties of functions of bounded variation and the statistical behavior of hyperuniform point processes. We establish several characterization formulas for the jump part of the gradient of a bounded variation function, extending and unifying previous results by Beretti--Gennaioli and Dávila. In particular, we provide new expressions for the $L^2$-jump of the gradient using both difference quotients and Fourier transform methods. Furthermore, we connect these analytic structures to the theory of hyperuniform point processes. By analyzing the variance of linear statistics associated with bounded variation functions, we provide asymptotic estimates that depend on the specific classification of the hyperuniformity of the point process. The results show how the regularity and jump discontinuities of a function dictate the growth rate of fluctuations in point processes. Finally, we introduce an averaged quadratic BMO-type oscillation functional over translated and rotated cube partitions, similar to the one recently studied by Ambrosio et al., and prove, using results from point process, that it converges to an explicit dimensional constant times the $L^2-$jump, giving in particular a further new characterization of the perimeter of a set.

math.CA↗

arXiv2018

Existence of quasicrystals and universal stable sampling and interpolation in LCA groups

We characterize all the locally compact abelian (LCA) groups that contain quasicrystals (a class of model sets). Moreover, we describe all possible quasicrystals in the group constructing an appropriate lattice associated with the cut and project scheme that produces it. On the other hand, if an LCA group G admits a simple quasicrystal, we prove that recent results of Meyer and Matei for the case of the n-dimensional Euclidean space can be extended to G. More precisely, we prove that simple quasicrystals are universal sets of stable sampling and universal sets of stable interpolation in generalized Paley-Wiener spaces.

math.CA↗

arXiv2006

Convergence of iterated Aluthge transform sequence for diagonalizable matrices

Given an $r\times r$ complex matrix $T$, if $T=U|T|$ is the polar decomposition of $T$, then, the Aluthge transform is defined by $$ Δ(T)= |T|^{1/2} U |T |^{1/2}. $$ Let $Δ^{n}(T)$ denote the n-times iterated Aluthge transform of $T$, i.e. $Δ^{0}(T)=T$ and $Δ^{n}(T)=Δ(Δ^{n-1}(T))$, $n\in\mathbb{N}$. We prove that the sequence $\{Δ^{n}(T)\}_{n\in\mathbb{N}}$ converges for every $r\times r$ {\bf diagonalizable} matrix $T$. We show that the limit $Δ^{\infty}(\cdot)$ is a map of class $C^\infty$ on the similarity orbit of a diagonalizable matrix, and %of class $C^\infty$ on the (open and dense) set of $r\times r$ matrices with $r$ different eigenvalues.

math.FA↗

arXiv2005

The Schur-Horn theorem for operators and frames with prescribed norms and frame operator

Let $\mathcal H$ be a Hilbert space. Given a bounded positive definite operator $S$ on $\mathcal H$, and a bounded sequence $\mathbf{c} = \{c_k \}_{k \in \mathbb N}$ of non negative real numbers, the pair $(S, \mathbf{c})$ is frame admissible, if there exists a frame $\{f_k \}_{k \in \mathbb{N}} $ on $\mathcal H$ with frame operator $S$, such that $\|f_k \|^2 = c_k$, $k \in \mathbb {N}$. We relate the existence of such frames with the Schur-Horn theorem of majorization, and give a reformulation of the extended version of Schur-Horn theorem, due to A. Neumann. We use it to get necessary conditions (and to generalize known sufficient conditions) for a pair $(S, \mathbf{c})$, to be frame admissible.

math.FA↗