P. Leonetti

activity

20122026

most citedOn the notions of upper and lower density

20 citations · 109 across the 55 of their papers we have counts for

collaborators

Showing 2020Show all

8 papers · 1 filter

math.CA2020

A Characterization of Cesaro Convergence

Paolo Leonetti

We show that a real bounded sequence $(x_{n})$ is Cesàro convergent to $ℓ$ if and only if the sequence of averages with indices in $[α^{k}, α^{k + 1})$ converges to $ℓ$ for all $α>1…

math.FA2020

Tauberian theorems for ordinary convergence

Paolo Leonetti

We show that a real sequence $x$ is convergent if and only if there exist a regular matrix $A$ and an $F_{σ δ}$ -ideal $I$ on $N$ such that the set of subsequences…

math.FA2020★ 4 cited

Turnpike in infinite dimension

Paolo Leonetti, Michele Caprio

Let $Φ$ be a correspondence from a normed vector space $X$ into itself, let $u : X \to R$ be a function, and $I$ be an ideal on $N$ . Also, assume that the…

math.CA2020

Convergent subseries of divergent series

Marek Balcerzak, Paolo Leonetti

Let $X$ be the set of positive real sequences $x = (x_{n})$ such that the series $\sum_{n} x_{n}$ is divergent. For each $x \in X$ , let $I_{x}$ be the collectio…

math.FA2020★ 1 cited

A characterization of $(I, J)$ -regular matrices

Jeff Connor, Paolo Leonetti

Let $I, J$ be two ideals on $N$ which contain the family $Fin$ of finite sets. We provide necessary and sufficient conditions on the entries of…

math.NT2020★ 8 cited

On the density of sumsets

Paolo Leonetti, Salvatore Tringali

Recently introduced by the authors in [Proc. Edinb. Math. Soc. 60 (2020), 139-167], quasi-densities form a large family of real-valued functions partially defined on the power set…