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Leandro Zuberman

Publications and source records attributed to Leandro Zuberman.

5 recordsLinked to original sources
arXiv2026

On the spectra of Cantor measures

We consider Cantor measures on the line, with contraction factor $N^{-1}=p^{-\alpha}$ (where $p$ a positive prime, $\alpha$ a positive integer) and $m$ positive integer digits lying in distinct residue classes modulo $N$. We obtain a complete characterization of maximal orthogonal sets of exponentials in $L^2(\mu)$, for a class of such measures $\mu$. It is proved that the $n+1$-th digit in the base-$N$ expansion of frequencies in a maximal orthogonal set, with the first $n$ digits prescribed, has $m$ possible values. In consequence, there are a correspondence between labelings of the $m$-homogeneous rooted tree and maximal orthogonal sets of frequencies.

math.CA↗
arXiv2019

Measures with specified support and arbitrary Assouad dimensions

We show that if the upper Assouad dimension of the compact set $E\subseteq \mathbb{R}$ is positive, then given any $D>\dim_{A}E$ there is a measure with support $E$ and upper Assouad (or regularity) dimension $D$. Similarly, given any $0\leq d<\dim_{L}E,$ there is a measure on $E$ with lower Assouad dimension $d$.

math.CA↗
arXiv2011

On the lattice structure of probability spaces in quantum mechanics

Let C be the set of all possible quantum states. We study the convex subsets of C with attention focused on the lattice theoretical structure of these convex subsets and, as a result, find a framework capable of unifying several aspects of quantum mechanics, including entanglement and Jaynes' Max-Ent principle. We also encounter links with entanglement witnesses, which leads to a new separability criteria expressed in lattice language. We also provide an extension of a separability criteria based on convex polytopes to the infinite dimensional case and show that it reveals interesting facets concerning the geometrical structure of the convex subsets. It is seen that the above mentioned framework is also capable of generalization to any statistical theory via the so-called convex operational models' approach. In particular, we show how to extend the geometrical structure underlying entanglement to any statistical model, an extension which may be useful for studying correlations in different generalizations of quantum mechanics.

quant-ph↗